a. I only b. II only c. III only d. II and III only e. I, II and III

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1 AP Statistics Final Review - Part I Name SOLUTIONS Per MULTIPLE CHOICE. Circle the best answer for each question. 1. We collect this data from 50 female college students. Which is categorical? a. Eye color b. head circumference c. hours of homework last week d. number of siblings e. height 2. Which of the following variables is quantitative? a. A person s gender b. A person s political affiliation c. Breed of dog d. The number of people on a jury e. The outcome of a coin toss 3. Which of the following variables would most likely follow a Normal model? a. Heights of students in an English class b. Home prices c. Baseball player salaries d. IQ scores e. Eye color of a group of nurses 4. An animal shelter has kept the above data records for the past 20 years. If they want to show the trend in the number of dogs they have housed over these years, what kind of plot should they make? a. Boxplot b. timeplot c. bar graph d. pie chart e. histogram 5. Which is true of the data shown in the histogram? I. The distribution is skewed to the right II. The mean is probably smaller than the median III. We should use median and IQR to summarize these data a. I only b. II only c. III only d. II and III only e. I, II and III 6. Two sections of a class took the same quiz. Section A had 20 students who had a mean score of 82, and Section B had 12 students who had a mean score of 88. Overall, what was the approximate mean score for all students on the quiz? 20(82) + 12(88) = a b c d. None of these e. Cannot be determined 7. The ages of people attending the opening show of a new movie are summarized in the ogive shown. Estimate the IQR of the ages. a. 5 b. 13 c. 21 d. 30 e. 37 Q = 25th percentile 30 1 Q = 75th percentile 43 3 IQR = = 13

2 8. Suppose that a Normal model describes pulse rate in a particular age group. Maria has a standardized score (zscore) of This means that Maria a. Has a pulse rate that is 1.5 times the average for her age group b. Has a pulse rate 1.5 beats above average for her age group c. Has a pulse rate 1.5 standard deviations above average for her age group d. Has a standard deviation of 1.5 e. None of the above 9. Elizabeth takes two exams, one in French and one in Math. In French, the class average was 78 and the standard deviation was 6. In Math, the class average was 74 and the standard deviation was 8. Elizabeth scored 86 on both exams. On which exam did she perform better relative to the rest of her class? a. She performed better in Math zfrench = = 1.33 (1 std. dev. above the mean) b. She performed better in French c. She performed equally well in both classes zmath = = 1.5 (1 std. dev. above the mean) 8 2 d. We would need to know the scores of all the students in each class to answer this question e. The scores can t be compared since they are from two different distributions 10. The five-number summary of credit hours for 24 students is Min Q 1 Median Q 3 Max Which statement is true? a. There are no outliers in the data b. There is at least one low outlier in the data c. There is at least one high outlier in the data d. There are both low and high outliers in the data e. None of the above lower fence: upper fence: Q 1.5( IQR) Q + 1.5( IQR) (18 15) (18 15) = 10.5 = If we want to discuss any gaps and clusters in a data set, which of the following should not be chosen to display the data set? DOESN T SHOW GAPS/CLUSTERS a. Histogram b. stem-and-leaf plot c. boxplot d. dotplot e. any of these would work 12. Which of the following summaries are changed by adding a constant to each data value? I. The mean II. The median III. The standard deviation a. I only b. III only c. I and II d. I and III e. I, II and III

3 13. Which of the following values change when a data set is multiplied by a constant? I. Mean II. Maximum III. IQR a. I only b. II only c. III only d. I and II only e. I, II and III 14. A store is keeping track of the payment method of its customers purchases (credit card, check, etc.). Which graph would be most appropriate for displaying the data they collect? CATEGORICAL VARIABLE a. histogram b. boxplot c. timeplot d. stem-and-leaf plot e. pie chart 15. Which is true of the data shown in the histogram? I. The distribution is approximately symmetric II. The mean and median are approximately equal III. The median and IQR summarize the data better than the mean and standard deviation a. I only b. II only c. I and II only d. I and III only e. I, II and III SHORT ANSWER. Answer each question as completely as possible. 16. A manufacturer claims that lifespans for their copy machines (in months) have a mean of 42 months and a standard deviation of 7 months, and can be described by a Normal model N(42, 7). a. Draw and clearly label the model according to the rule b. What percent of the copiers are expected to fail before 36 months? z = = PX ( < 36) =.1949 c. The company is going to provide a warranty that will replace copiers which last less than a certain number of months. How many months should their warranty cover if they only want to replace 10% of copiers? x = 7 x = months

4 17. One day a store tracked the way shoppers paid for their purchases. Their data are summarized in the table: Cash Check Charge Total Male Female Total a. Find the marginal distribution of payment type (in percents). Cash _36/100 = 36% Check _22/100 = 22% Charge 42/100 = 42% b. Find the conditional distribution of payment type among female shoppers. Cash _18/60 = 30% Check _12/60 = 20% Charge _30/60 = 50% c. Is there evidence of an association between gender and method of payment? Explain. There does appear to be an association, since women are less likely to use cash and more likely to use a credit card than male customers. 18. Repair bills. An automobile service shop recorded data on all of the repairs made for their customers last week. They kept track of the problem reported, time required for the repair, name of service technician, and cost in dollars. a. Discuss as many of the W s (Who, What, Where, Why, When, How) as possible. Who: repairs made What: problem, time, technician, cost Where: unknown Why: unknown When: unknown How: kept service records b. The shop reported the summary statistics shown for the variable of cost ($). Were any of the bills outliers? Show how you made your decision. Min 27 lower fence: upper fence: Q1 88 Q1 1.5( IQR) Q3+ 1.5( IQR) Median (308 88) (308 88) Q3 308 = $242 = $638 Max 1442 Mean 284 There is at least one upper outlier, since the maximum Std Dev 140 is above the upper fence. There are no lower outliers. c. A customer who received a bill of $300 complained that her bill was outrageous compared to the other customers at the shop. Would you agree this as an extremely high bill? Explain. No two possible explanations (either would be correct): The bill is lower than the 3 rd quartile, which means it is not that unusual. It falls in the middle 50% of bills The bill is not unusual since it falls less than two standard deviations above the mean.

5 AP Statistics Final Review #2- Part II Name SOLUTIONS Per MULTIPLE CHOICE. Circle the best answer for each question. 1. Which scatterplot shows a strong association between two variables even though the correlation is probably near zero? a. b. c. d. e. 2. A least squares line of regression has been fitted to a scatterplot; the model s residual plot is shown. Which is true? a. The linear model is poor because some residuals are large. b. The linear model is poor because the correlation is near 0. c. A curved model would be better. d. The linear model is appropriate. e. None of the above. 3. The residual plot for a linear model is shown. Which is true? a. The linear model is okay because approximately the same number of points are above the line as below it. b. The linear model is okay because the association between the two variables is fairly strong. c. The linear model is no good because the correlation is near 0. d. The linear model is no good because some residuals are large. e. The linear model is no good because of the curve in the residuals. 4. All but one of these statements contain a mistake. Which could be true? a. There is a correlation of.51 between the gender of American workers and their income. GENDER IS A CATEGORICAL VARIABLE. b. We found a high correlation (r = 1.27) between teacher ratings and class size. CORRELATION HAS TO BE BETWEEN -1 AND +1 c. The correlation between planting rate and yield of corn is.35 bushels. CORRELATION SHOULD NOT HAVE UNITS d. There is a correlation of 0.53 between hours of sleep and percent correct on a test. e. The correlation between a baseball player s hair color and his salary is HAIR COLOR IS A CATEGORICAL VARIABLE 5. A tree grows by 4 inches each year. This growth is ADD THE SAME # EACH TIME = LINEAR a. quadratic b. linear c. logarithmic d. exponential e. power

6 6. A tree s height increases by five percent each year. This growth is MULTIPLY BY THE SAME # EACH TIME = EXPONENTIAL a. quadratic b. linear c. logarithmic d. exponential e. power 7. Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from some other, possibly hidden, factor. This is an example of a. leverage b. extrapolation c. a lurking variable d. regression e. an outlier 8. If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and the correlation (r)? a. b will increase, and r will decrease. OLD b. b will decrease, and r will increase. NEW c. Both will increase. d. Both will decrease. e. Both will remain the same. 9. The relationship between age and height in children probably has a correlation which is AS KIDS GET OLDER, THEY GROW TALLER, BUT IT S NOT A PERFECT CORRELATION a. near +0.7 b. near 0 c. near -1.0 d. exactly +1.0 e. near The model str = ( dia) can be used to predict the breaking strength of a rope (in pounds) from its diameter (in inches). According to this model, how much force should a rope one-half inch in diameter be able to withstand? str = (.5) str = str = 22 2 str = (22) = 484 a. 4.7 lbs b. 16 lbs c. 22 lbs d. 256 lbs e. 484 lbs 11. A particular student scored 1830 on the SAT. If we created a model which used SAT scores to predict college GPA, the student would want to have NEGATIVE RESIDUAL = POINT IS BELOW THE LINE (ACTUAL VALUE IS LOWER THAN PREDICTED) POSITIVE RESIDUAL = POINT IS ABOVE THE LINE (ACTUAL VALUE IS HIGHER THAN PREDICTED) REMEMBER THAT RESIDUALS HAVE TO DO WITH PREDICTED VALUES (GPA, NOT SAT SCORE) a. A negative residual, because that means the student s SAT score is higher than we would predict with the model. b. A positive residual, because that means the student s SAT score is higher than we would predict with the model. c. A negative residual, because that means the student s college GPA is higher than we would predict with the model. d. A residual equal to zero, because that means the student s midterm and college GPA were exactly the same. e. A positive residual, because that means the student s college GPA is higher than we would predict with the model.

7 SHORT ANSWER. Answer each question as completely as possible. 12. Storks. Data show that there is a positive association between the population of 17 European countries and the number of stork pairs in those countries. a. Briefly explain what positive association means in this context. Countries with more people tend to have more storks. b. Wildlife advocates want the number of storks to increase, so they approach the governments of these countries to encourage their citizens to have children so that the countries populations will grow. As a statistician, what do you think of this plan? Explain briefly. It doesn t make sense it is likely that there is another reason for the association other than causation. For example, it could be that countries with larger land mass or better climate have more people and also have more storks. 13. Associations. For each pair of variables, indicate what association you expect: positive (+), negative (-), curved (C) or none (N). - _ a student s number of absences & the student s grade point average -_ the time it takes a person to complete an aptitude test & the hours of sleep they got the night before C_ a person s age & the strength of their grip N_ an adult s height & and their IQ score +_ a person s height & arm length 14. Penicillin. Doctors studying how the human body processes medication inject some patients with penicillin, and then monitor the concentration of the drug (in units/cc) in the patients blood for seven hours. The data are shown in the scatterplot. First they tried to fit a linear model for concentration(y) v. time(x). The regression analysis and residuals plot are shown. a. Write the equation of the least squares regression line. Define any variables used. conc = ( time) b. Interpret the slope of the line. For every additional hour, the concentration decreases by 5.96 units/cc on average.

8 c. Interpret the intercept of the line. The predicted initial concentration before any time has passed is 40.3 units/cc. d. What is the correlation between time and concentration? Interpret this correlation. r =.908 =.953 There is a strong negative positive association between time and concentration. (Remember that the slope was negative!) e. Interpret the R 2 value. 90.8% of the variability in concentration can be explained by the relationship with time. f. Use the model to estimate what the concentration of penicillin will be after 4 hours yˆ = (4) = 16.5 units / cc g. The value of s in the output above is Interpret this value in the context of the problem. This is the standard deviation of the residuals. On average, the predicted values are units/cc away from the actual values. h. Is that estimate likely to be accurate, too low or too high? Explain. Since the residual in that area is expected to be negative (based on the graph on the previous page), the prediction is likely to be too high. Negative residual point below line: Now the researchers try a new model, using the re-expression log(concentration) v. time. Examine the regression analysis and the residuals plot below. i. Explain why you think this model is better than the original linear model. This residual plot doesn t have a pattern, while the first residual plot was curved. j. Using this new model, estimate the concentration of penicillin after 4 hours. log conc = (4) log conc = conc = = / units cc

9 AP Statistics Final Exam Review #1 - Part III Name Per MULTIPLE CHOICE. Circle the best answer for each question. 1. The owner of a car dealership planned to develop strategies to increase sales. He hoped to learn the reasons why many people who visit his car lot do not eventually buy a car from him. For one month he asked his sales staff to keep a list of the names and addresses of everyone who came in to test drive a car. At the end of the month he sent surveys to the people who did not buy the car, asking them why. About one-third of them returned the survey, with 44% of those indicating that they found a lower price elsewhere. Which is true? I. The population of interest is all potential car buyers POPULATION = EVERYONE WE WANT TO KNOW ABOUT II. This survey design suffered from non-response bias 56% OF THOSE SURVEYS DIDN T RESPOND III. Because it comes from a sample 44% is a parameter, not a statistic STATISTICS DESCRIBE SAMPLES; PARAMETERS DESCRIBE THE POPULATION a. I only b. II only c. I and II only d. II and III only e. I, II and III 2. A factory has 20 assembly lines producing a popular toy. To inspect a representative sample of 100 toys, quality control staff randomly selected 5 toys from each line s output. Was this a simple random sample? a. Yes, because the toys were selected at random. b. Yes, because each toy produced had an equal chance to be selected. c. Yes, because a stratified sample is a type of simple random sample. d. No, because not all combinations of 100 toys could have been chosen IN AN SRS, ALL POSSIBLE COMBINATIONS OF INDIVIDUALS ARE EQUALLY LIKELY e. No, because toys do not come off the assembly line at random. 3. Does regular exercise decrease the risk of cancer? A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. This is a a. survey b. retrospective study c. prospective study FOLLOWED OVER TIME d. randomized experiment e. matched experiment 4. Which is important in designing a good experiment? I. Randomization in assigning subjects to treatments. II. Control of potentially confounding variables. III. Replication of the experiment on a sufficient number of subjects. THESE ARE THE THREE PRINCIPLES OF EXPERIMENTAL DESIGN a. I only b. I and II c. I and III d. II and III e. I, II and III 5. Can watching a movie temporarily raise your pulse rate? Researchers have 50 volunteers check their pulse rates. Then they watch an action film, after which they check their pulse rates once more. Which aspect of experimentation is present in this research? THEY SHOULD HAVE DONE THESE THINGS, BUT DIDN T a. a placebo b. blinding c. randomization d. a control group e. none of these 6. In an experiment the primary purpose of blocking is to reduce

10 YOU BLOCK SO THAT THE VARIABLE YOU ARE BLOCKING FOR DOESN T GET IN THE WAY a. bias b. confounding c. randomness d. undercoverage e. variation 7. To check the effect of cold temperatures on the battery s ability to start a car, researchers purchased a battery from Sears and one from NAPA. They disabled a car so it would not start, put the car in a warm garage, and installed the Sears battery. They tried to start the car repeatedly, keeping track of the total time that elapsed before the battery could no longer turn the engine over. Then they moved the car outdoors where the temperature was below zero. After the car had chilled there for several hours the researchers installed the NAPA battery and repeated the test. Is this a good experimental design? a. Yes b. No, because the car and the batteries were not chosen at random. c. No, because they should have tested other brands of batteries, too. d. No, because they should have tested more temperatures. e. No, because temperature is confounded by brand. 8. Twenty dogs and twenty cats were subjects in an experiment to test the effectiveness a new flea control chemical. Ten of the dogs were randomly assigned to an experimental group that wore a collar containing the chemical, while the others wore a similar collar without the chemical. The same was done with the cats. After 30 days, veterinarians were asked to inspect the animals for fleas and evidence of flea bites. This experiment is a. Completely randomized with one factor: the type of collar b. Completely randomized with one factor: the species of animal c. Randomized block with one factor (type of collar), blocked by species d. Randomized block with one factor (species), blocked by type of collar e. Completely randomized with two factors: species and type of collar 9. Which statement about bias is true? I. Bias results from random variation and will always be present. BIAS IS DUE TO BAD SAMPLING METHODS II. Bias results from a sampling method likely to produce samples that do not represent the population. III. Bias is usually reduced when the sample size is larger. A BAD SAMPLING METHOD IS JUST AS BAD FOR A LARGE SAMPLE AS IT IS FOR A SMALL ONE a. I only b. II only c. III only d. I and II only e. II and III only 10. A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next 5 free throw attempts? I. Let 0, 1 represent making the first shot, 2, 3 represent making the second shot,, 8, 9 represent making the fifth shot. Generate five random numbers 0-9, ignoring repeats. II. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate 5 random numbers 0-9 and count how many numbers are in 3-9. III. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats. REPEATS ARE OK SINCE EACH NUMBER DOESN T REPRESENT A PARTICULAR PERSON OR ITEM a. I only b. II only c. III only d. II and III e. I, II and III

11 11. Members of the dance team, wearing their dance uniforms, conduct a survey in which they ask students whether they think dance should be considered a sport. This survey is flawed mainly because of a. undercoverage b. voluntary response bias c. nonresponse d. response bias (caused by the interviewer effect) e. response bias (caused by the wording effect) 12. A TV news call-in poll resulted in 88% of people responding that they are very concerned about the state of education in America. This survey is flawed mainly because of a. undercoverage b. voluntary response bias c. nonresponse d. response bias (caused by the interviewer effect) e. response bias (caused by the wording effect) SHORT ANSWER. Answer each question as completely as possible. 12. M&M s. The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter M, 10% show the symbol &, and the rest just say Try again. When you collect a set of three symbols M, & and M, you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Use a simulation to find out. a. Describe how you will use a random number table to conduct this simulation. I will use the numbers to represent bags of M&Ms will represent those containing M, will represent those containing &, and will represent those containing Try Again. I will go across the random number table choosing 2-digit numbers and recording the game piece earned on each. Repeats will be allowed. I will stop when I have 2 M s and one &, and record how many bags it took to reach that point. b. Carefully label your simulation for 2 trials Trial Simulation Outcome # bags M M & # bags & & & M M c. State your conclusion. Based on my simulation, I would expect it to take (6 + 10)/2 = 8 bags on average to win a free one. 13. Candy packaging. Marketing researchers wonder if the color and type of a candy s packaging may influence sales of the candy. They manufacture test packages for chocolate mints in three colors (white, green and silver) and three types (box, bag, and roll). Suspecting that sales may depend on a combination of package color and type, the researchers prepare nine different packages, then market them for several weeks in convenience stores in various locations. a. What are the experimental units? candy packages b. How many factors are there? 2 c. How many treatments are there? 9 d. What is the response variable? sales

12 14. Moods. A headline in the New York Times announced Research shows running can alter one s moods. The article reported that researchers gave a Personality Assessment Test to 231 males who run at least 20 miles a week, and found statistically significant personality differences between the runners and the male population as a whole. a. Explain what statistically significant means in this context. The difference in mood between runners and the male population is to big to be attributed to random chance (or natural variation). b. Do you think the newspaper s headline was appropriate? Explain. No the study only shows that running and mood have an association, not that running actually causes an improvement in mood. It could be that happier people are the ones who have the energy to get out and run. 15. Public opinion. A member of the City Council described in #15 proposes that a new study be conducted, since their telephone poll was invalid. They decide that they also want to change their sampling design. Below are some of the methods that are proposed to sample local residents. Match each with one of the listed sampling techniques. _7 a) Place an announcement in the newspaper asking people to call their council representatives to register their opinions. Council members will tally the calls they receive. _2 b) Have each council member survey 50 friends, neighbors, or co-workers _4 c) Have the Board of Elections assign each voter a number, then select 400 of them using a random number table. _5 d) Randomly pick 50 voters from each election district _6 e) Call every 500 th person in the phone book Cluster Convenience Multistage Simple random (SRS) Stratified Systematic Voluntary response _3 f) Randomly pick several city blocks, then randomly pick 10 residents from each block _1 g) Randomly select several city blocks; interview all the adults living on the block 16. Dog food. The Acme Dog Food Company has developed a new formula which they think will give dogs a shinier coat. They would like to compare this new food to their old food and have hired you as a consultant. You have 50 dogs available for testing. Design an appropriate experiment for this purpose. Include an explanation of how you will carry out your randomization. Random Allocaton Group 1 25 dogs Group 2 25 dogs Old food Old food Compare shininess of coat To randomize, I would assign each dog a number from 1-50 and then use a random number generator to choose the first 25 dogs, which will go in the first group. The remainder will be in the second group.

13 AP STATISTICS PART IV REVIEW #1 NAME SOLUTIONS PER MULTIPLE CHOICE. Circle the best answer to each question. Use the following information for questions 1-2: In an AP Statistics class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. 46% of students eat breakfast and also floss their teeth. 1. What is the probability that a student from this class eats breakfast but does not floss their teeth? a. 9% b. 11% c. 34% d. 57% e. 91% 2. What is the probability that a student from this class neither eats breakfast nor flosses their teeth? a. 9% b. 11% c. 34% d. 57% e. 91% 3. Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability that they are both juniors or both seniors? Both juniors a b c d e A fair coin has come up heads 10 times in a row. The probability that the coin will come up heads on the next flip is a. less than 50%, since tails is due to come up. b. 50%. Since the flips are independent c. greater than 50%, since it appears that we are on a streak of heads. d. It cannot be determined. 5. According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computer in What is the probability that of five randomly selected U.S. households, exactly two owned a computer in 2001? Binomial, n = 5, p =.565 PX 2 3 ( = 2) = 5C2(.565) (.435) =.263 a b c d e According to the National Telecommunication and Information Administration, 50.5% of U.S. households had internet access in What is the probability that of five randomly selected U.S. households, at least one had internet access in 2001? P B = F.09 Both seniors 5 (at least one had internet) = 1 P(none had internet) = 1 (.495) =.970 a b c d e

14 7. Which of these has a Binomial model? (looking for a number of successes in a fixed # of Bernoulli trials) a. The number of people we survey until we find someone who has taken Statistics b. The number of people who have taken Statistics among a group of 20 college students c.. The number of aces in a five-card poker hand d. The number of sodas students drink per day e. The distribution of the heights of a the members of a choir 8. Which of these has a Geometric Model? (looking for the first success in a set of Bernoulli trials) a. The number of people we survey until we find someone who has taken Statistics b. The number of people who have taken Statistics among a group of 20 college students c.. The number of aces in a five-card poker hand d. The number of sodas students drink per day e. The distribution of the heights of a the members of a choir 9. A company that sells batteries claims that 98% of their batteries are in working order. How many batteries would you expect to buy, on average, to find one that does not work? 1 1 geometric µ = 50 p =.02 = a. 98 b. 102 c. 45 d. 980 e Some marathons allow two runners to split the marathon by each running a half marathon. Alice and Sharon plan to split a marathon. Alice s half-marathon times average 92 minutes with a standard deviation of 4 minutes, and Sharon s half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women s half-marathon times are independent. The expected time for Alice and Sharon to complete a full marathon is = 188 minutes. What is the standard deviation of their total time? σ + = + = S A a. 2 minutes b. 4.5 minutes c. 6 minutes d. 20 minutes e. It cannot be determined SHORT ANSWER. Show all work required for each problem. 11. Passing the test. Assume that 70% of teenagers who go to take the written driver s license test have studied for the test. Of those who study, 95% pass; of those who do not study, 60% pass. What is the probability that a teenager who passes the written driver s license test did not study for the test? (Hint: Use a tree diagram).7.3 studied didn't study pass = fail = pass = 0.18 fail = Pdidntstudy ( ' pass ) = =

15 12. Luxury cars. According to infoplease, 18.8% of the luxury cars sold in 2003 were silver. A large car dealership typically sells 50 luxury cars a month. a. Explain why you think that the luxury car sales can be considered Bernoulli trials. Two possible outcomes: silver or not silver Each sale is independent: the sample is less than 10% of the population (more than 500 cars are produced), the cars are sold separately so the sales should be independent The probability of success (18.8%) remains the same for every sale b. What is the probability that the fifth luxury car sold is the first silver one? Geometric: c.. What is the probability that at least 5 of the luxury cars sold at the dealership in a particular month were silver? Binomial with n = 50 & p =.188 PX ( 5) = 1 [ PX ( = 0) + PX ( = 1) PX ( = 4)] = 1 [( C (.188) (.812) C (.188) (.812) ] = d. What is the average number of silver cars sold at the dealership in a particular month? What is the standard deviation? µ = np = 50(.188) = 9.4 silver cars 4 (.812) (.188) = σ = np(1 p) = 50(.188)(.812) = 2.76 silver cars 13. The annual income in a particular region varies according to a Normal model with mean of $57,000 and standard deviation of $6,350. Find each of the following probabilities: a. a randomly selected household has an annual income above $75, z = = PX ( > 75000) = =.0023 $57K $75K b. a randomly selected household has an annual income below $50,000 $50K $57K z = = PX ( < 50000) =.1357 c. a randomly selected household has an annual income between $45,000 and $65,000 $45K $65K z45k = = z65k = = P(45000 < X < 65000) = =.8668

16 14. Bowling. A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of 9 pins, while the women had a mean score 144 pins and standard deviation 12 pins. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round. a. On average, how much do expect the man to win by (hint: what will be the difference between the two scores?) EM ( W) = = 10 pins b. What will be the standard deviation of the difference in the scores? SD M 2 2 ( W ) = = 15 pins c. What assumption did you have to make in determining the standard deviation? We had to assume that the men s and women s scores vary independently.