Midterm Review Summer 2009 Chapters 1 7 Stat 111

Transcription

1 Midterm Review Summer 2009 Chapters 1 7 Stat 111 Name FORM A Directions: Read each question carefully and answer as clearly as possible. 1. A book store wants to estimate the proportion of its customers who buy murder mysteries. A random sample of 76 customers is observed at the checkout counter and the number purchasing murder mysteries is recorded. a. Identify the variable of interest. b. Is the variable quantitative or qualitative? c. What is the implied population? 2. For information in parts (a) through (e) below, list the type of measurement as qualitative or quantitative. A restaurant manager is developing a clientele profile. Some of the information for the follows: profile a. Gender of diners. b. Size of group dining together. c. Time of day the last diner of the evening departs. d. Age grouping: young, middle age, senior e. Length of time a diner waits for a table. 3. Categorize the style of gathering data (sample survey, randomized experiment, census survey) for the following situation. a. Consider all the students enrolled at UVM this semester and report the age of each student. b. Select a sample of new pickup trucks and count the number of manufacturer defects in each of the truck. c. Teach one section of English composition using a specific word processing package and teach another without using any computerized word processing. Count the number of grammar errors made by students in each section on a final draft of a 20 page term paper. 4. A random sample of 18 airline carry-on luggage bags gave the following weights (rounded to the nearest pound) a. Find the mean. b. Find the median. c. Find the mode. d. Find the 5% trimmed mean.

2 5. To determine monthly rental prices of apartment units in the San Francisco area, samples were constructed in the following ways. Categorize each sampling technique described as cluster, convenience, simple random, stratified, or systematic. a. Number of all the units in the area and use a random number table to select the apartment to include in the sample. b. Divide the apartments units according to number of bedrooms and then sample from each of the groups. c. Select 5 Zip codes at random and include every apartment unit in the selected Zip codes. d. Look in the newspaper and consider the first sample of apartment units that list rent per month. e. Call every 50 th apartment complex listed in the yellow pages and record the rent. 6. Professor Hill in the Music Department kept a list of the number of students visiting his office each week for two semesters (30 weeks). The results were: a. Find the class width using five classes. b. Construct a frequency table c. Construct a histogram. Make sure to give a title and label the axes. d. Is the data symmetric, skewed right, or skewed left. 7. Give an example of how you could collect data on the smoking habits of UVM students by using an observational study that doesn t involve a survey. 8. A random sample of 7 Northern Pike from Taltson Lake (Canada) gave the following lengths rounded to the nearest inch. a. Find the range. b. Find the sample mean. c. Find the sample variance. d. Find the sample standard deviation

3 9. You roll two fair dice (a blue one and a yellow one). a. Find P(even # on the blue die and 3 on the yellow die) b. Find P(3 on the blue die or even # on the yellow die) c. Find P(3 on the blue die and even # on the yellow die or even # on the blue die and 3 on the yellow die) 10. An urn contains 12 balls identical in every respect except color. There are 3 red balls, 7 green balls, and 2 blue balls. a. You draw two balls from the urn, but replace the first ball before drawing the second. Find P(first ball is red and the second ball is green). b. Repeat part (a), but do not replace the first ball before drawing the second. c. Repeat part (a), but also draw a third ball not replacing after any of the draws. Find P(first ball is red and the second ball is green and the third ball is blue). Hint: Think of P(first ball is red and second ball is green) as a single event you already know the probability of this from part (a). 11. A random sample of 317 new Smile Bright electric toothbrushes showed that 19 were defective. a. Estimate the probability that a randomly chosen new Smile Bright electric toothbrush is defective. b. Estimate the probability that a randomly chosen new Smile Bright electric toothbrush is not defective. c. Either an electric toothbrush is defective or not. What is the sample space in this problem? Do the probabilities assigned to the simple events in the sample space add up to one? 12. Of all college freshmen who try out for the track team, each one only has a 30% chance of making the team. Suppose that 15 freshmen try out for the team and X is the number that make the team. X has a binomial distribution with a. n = b. p = c. q = d. What is the expected or average value of X? e. What is the standard deviation of X? (Round to two decimal places.) 13. Of those people who lose weight on a diet, 90% gain all the weight back. In a random sample of 12 dieters who have lost weight, what is the probability of each of the following? a. All 12 gain the weight back. (Round your answer to three decimal places.) b. At least 9 gain the weight back. (Round your answer to three decimal places.) c. No more than 6 gain the weight back. (Round your answer to three decimal places.)

4 14. A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walkin customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results follow. Walk-In TV Ad Referred Total Not Satisfied Neutral Satisfied Very Satisfied Total Assume the sample represents the entire population of customers. Find the probability that a customer is a. Not satisfied. b. Not satisfied and walk-in. c. Not satisfied, given referred. d. Very satisfied. e. Very satisfied, given referred. f. Very satisfied and TV ad. g. Very satisfied or TV ad. h. Based solely on the probabilities found above, are the events satisfied and referred independent or not? Explain. 15. Which of the following is most likely to not have a bell shaped distribution? Explain. a. Height in inches of a UVM student. b. Actual weight in ounces of a 12-oz can of dog food. c. Years attending UVM for an undergraduate student. d. SAT score for a 1 st year student at UVM. 16. From long experience, it is known that the time it takes to do an oil change and lubrication job on a vehicle has a normal distribution with mean µ = 18 minutes and standard deviation of σ = 5 minutes. a. What is the probability that it takes less than 14 minutes? Round your answer to four decimal places. b. What is the probability that it takes more than 16.5 minutes? Round your answer to four decimal places. c. What is the probability that it takes between 17 and 19 minutes? Round your answer to four decimal places. d. An auto service shop will give a free lube job to any customer who must wait beyond the guaranteed time to complete the work. If the shop does not want to give more than 5% of its customers a free lube job, then how long should the guarantee be? Round your answer to the nearest minute.

5 17. According to the Empirical Rule, for a distribution that is symmetrical and bell-shaped (in particular, for a normal distribution) approximately % of the data values will lie within three standard deviation of the mean? 18. Let X be the random variable that represents the length of time it takes a student to complete a take-home exam in a psychology class. After interviewing many students, it is found that X has an approximately normal distribution with mean of µ = 5.2 hours and standard deviation σ = 1.8 hours. a. Standardize the intervals. Round the z scores to two decimal places. o x 2.59 o 6.55 x o 2.59 x 6.55 b. Find the following probabilities. Round the values to four decimals. o P( x 2.59) o P(6.55 x) o P(2.59 x 6.55) c. 10% of the students were able to finish in under how many hours? Round your answer to three decimals. 19. Determine if the following scenarios have values which are statistics or parameters. a. The Nielson Company gathers data on the viewing habits of all Americans. To do this, the company randomly picks 2500 households and asks them to make a log of their TV viewing habits. Based on the data collected from the 2500 households, the Nielson Company determines that 87% of Americans are in love with Reality Television. b. United Academics, the faculty union at UVM, is interested in how often its members visit the union s website. To do this, the union asks each member to fill out a response card which they must include with their annual union dues. Based on the responses, union members visit the website an average of 12.4 times a year. 20. Suppose that x is a random variable found by taking a sample from a population which has a mean of µ = 40 and a standard deviation of σ = 12. Let x be the average of a sample of size n = 36. a. The distribution of x has a mean of what? b. The distribution of x has a standard deviation of what? c. Is the distribution of x guaranteed to be approximately normal?

6 21. Based on data collected from the last US Census, 64% of people living in the United States do not have a valid passport. Suppose that a random sample of size n = 100 people living in the US is chosen. Let ˆp be the proportion of the 100 people who do not have a valid passport. a. The distribution of ˆp has a mean of what? b. The distribution of ˆp has a standard deviation of what? c. Is the distribution of ˆp guaranteed to be approximately normal? d. Suppose that you randomly contact 100 individuals living in the United States. What is the probability that at most 70% have a valid passport? Round your answer to four decimal places. 22. According to the school board, 48% of all the voters in the district support a referendum banning the sale of soda during lunchtime. Suppose a principal is interested in the proportion who support the referendum in a group of 38 parents. Let ˆp be the proportion of the 38 parents who support the referendum. a. What is the mean of the distribution of ˆp? b. What is the standard deviation of the distribution of ˆp? Round your answer to three decimal places. c. What is the probability that the proportion of the group who support the referendum is no more than 30%? Round your answer to four decimal places. 23. The manufacturer of a coffee dispensing machine claims the actual amount dispensed into a cup has a normal distribution with mean µ = 7 ounces and standard deviation σ = 0.8 ounces. Suppose that n = 40 cups of coffee are measured and the average amount x is determined. a. What is the mean of the distribution of all possible x s? b. What is the standard deviation of the distribution of all possible x s? Round your answer to three decimal places. c. What is the probability that the average amount from the 40 cups is less than 6.8 ounces? Round your answer to four decimal places. d. What is the probability that the average amount from the 40 cups is more than 7.1 ounces? Round your answer to four decimal places. e. What is the probability that the average amount from the 40 cups is between 6.8 and 7.1 ounces? Round your answer to four decimal places.