Probability and Statistics Cycle 3 Test Study Guide

Transcription

1 Probability and Statistics Cycle 3 Test Study Guide Name Block 1. Match the graph with its correct distribution shape. The distribution shape is categorized as: A. Uniform B. Skewed to the right C. Normal D. Skewed to the left 2. Match each description to its level of measurement. Temperature inside the car on a hot day. Color of the new car. Fuel economy of a new car. Size of a new car (sub-compact, compact, mid-size, large) A. Nominal B. Ordinal C. Interval D. Ratio 3. Which of the following variables from a study about traffic at a gas station is NOT matched with the correct type of data? A. How Many Cars Are Getting Gas Qualitative B. Price of Gas Per Gallon Quantitative C. Gallons of Gas Pumped Quantitative D. Type of Gas Being Pumped (Diesel, High Octane, Etc.) - Qualitative 4. The durations of a random sample of 20 commercials are given below (in seconds). Find the mean, median, and mode of these durations A. Mean = B. Median = C. Mode = 1

2 5. A random sample of 150 salaried employees was asked how many hours per week they spend at work. The results follow, where x is the hours and f is the number of employees who spend that amount of time at work. Compute the sample standard deviation. x f After a fire drill at King s Fork High School, thirteen classrooms are randomly selected and all students in those classrooms are surveyed about their ideas for improving exit plans from their rooms. What type of sampling technique would be used to represent this data? 7. After a fire drill at King s Fork High School, thirteen students from each classroom are randomly selected and are surveyed about their ideas for improving exit plans from their rooms. What type of sampling technique would be used to represent this data? 8. After a fire drill at King s Fork High School, every fourth student re-entering the building is selected and surveyed about their ideas for improving exit plans from their rooms. What type of sampling technique would be used to represent this data? 9. After a fire drill at King s Fork High School, Mr. Payton surveys whichever students just happen to go past his room on their way back to class about their ideas for improving exit plans from their rooms. What type of sampling technique would be used to represent this data? 10. A survey was developed to estimate the average number of hours per week that teenagers spend reading. Every third teenager entering a library was surveyed, with a total of 2000 people being surveyed. The data showed that the mean number of times going to the library was 2.5 times per month. Which characteristic of the survey could create a bias in the results?. Decide whether the event is independent, dependent, both, or neither. 11. Selecting a club from a standard deck, replacing it, and then selecting a spade from the deck A. Independent B. Dependent C. Both D. Neither 12. Which events would be considered mutually exclusive? Assume we are referring to both things occurring in a single trial. A. Event A: Randomly select a female high school student. Event B: Randomly select a soccer player. B. Event A: Randomly select a vehicle that is a sedan. Event B: Randomly select a vehicle that is a SUV. C. Event A: Randomly select a 14-year-old student. Event B: Randomly select a student with blond hair. D. Event A: Randomly select a club from a standard deck of 52 cards. Event B: Randomly select a queen from a standard deck of 52 cards. 13. Jacob draws two cards from a standard deck of 52 cards. What is the probability of drawing two cards of the same value in a row? The cards are not replaced in the deck. 2

3 Use this table to answer the next three questions (14-16). A group of students were asked if they have a driver s license. The responses are listed in the table. Class Driver s License No Driver s License Total Junior Senior Total If a student is selected at random, what is the probability that he or she has a license given that the student is a senior? Round your answer to the nearest thousandth. 15. If a student is selected at random, what is the probability that he or she does not have a license and is a senior? Round your answer to the nearest thousandth. 16. If a student is selected at random, what is the probability that he or she has a license or is a junior? Round your answer to the nearest thousandth 17. The events A and B are mutually exclusive. If P(A) = 0.5 and P(B) = 0.34, what is P(A or B)? 18. If the probability of success is 0.37, find the probability of two failures in a row. 19. Imagine you have some odd-shaped dice numbered from 1 through the number of sides. Die 1 has 7 sides, die 2 has 11 sides, and die 3 has 14 sides. If you rolled each die 100 times, which die would be expected to have the MOST number of even rolls? 20. A study of movie-goers includes 75 people in the age bracket (42 of whom prefer action sample, find the probability of getting someone who is age or prefers action movies. 21. A study of movie-goers includes 75 people in the age bracket (42 of whom prefer action sample, find the probability of getting someone who is age and prefers action movies. 22. A study of movie-goers includes 75 people in the age bracket (42 of whom prefer action sample, find the probability of getting someone who is in the age group or the age group. 23. According to the empirical rule, for a distribution that is symmetric and bell-shaped (in particular, for a normal distribution), approximately of the data values will lie within 3 standard deviations on each side of the mean. YOU NEED TO KNOW ALL OF THESE PERCENTAGES!! 24. The number of miles on a car when a certain part fails is normally distributed, with a mean of 45,000 and a standard deviation of 3,000. What is the probability that a part will fail between 39,000 and 51,000 miles? 25. Find the area of the shaded region under the standard normal curve. The z-scores are and

4 26. A Geometry class has a mean score of 64.2 on a test, with a standard deviation of A World History class has a mean score of 78.5 on a test, with a standard deviation of 8.3. A student takes both tests and scores a 73 on the Geometry test and an 88 on the World History test. Compare the scores. A. The two scores are statistically the same. B. You cannot determine which score is better from the given information. C. A score of 88 on the History test was better. D. A score of 73 on the Geometry test was better. 27. At 97% confidence, what is the critical value, t c, of a sample size of 14? 28. From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, what is the margin of error? 29. What would be the minimum sample size needed to predict, within 3 miles, the distance the average commuter drives to work. Assume that the standard deviation is 6.89 miles and you want a 90% confidence level. 30. The sampling distribution of the mean becomes approximately normally distributed only when what is true?. 31. The central limit theorem states that the sampling distribution of the mean becomes more normally distributed as. 32. The central limit theorem states that the sampling distribution of sample means has a mean equal to the population. 33. The central limit theorem states that the sampling distribution of sample means has a standard deviation equal to the population. Use the following passage to answer the next two questions. A pizza delivery service claims that the mean delivery time is less than 24.9 minutes. A random sample of 60 customers has a mean of 24.8 minutes with a standard deviation of 4.6 minute. If α = 0.05, test the pizza delivery service s claim. 34. Using the above information, what are the null and alternate hypotheses? H 0 : H a : 35. Can you support the claim that the delivery time is less than 24.9 minutes? Why or why not? 36. The mean annual salary of a random sample of 62 American adults was $45,257, with a standard deviation of $6,920. Construct a 95% confidence interval for the population mean. Assume that the population is normally distributed In a random sample of 23 computers brought in for repairs, the mean cost of repairs was $149.00, with a standard deviation of $18. Construct a 95% confidence interval for the population mean. Assume that computer repair costs are normally distributed You wish to estimate, with 97.5% confidence and within 2.5% of the true population, the proportion of U.S. adults that think our political system is broken. Find the minimum sample size needed when a prior study found that 64% of U.S. adults think our political system is broken. 4

5 39. You wish to estimate, with 97.5% confidence and within 2.5% of the true population, the proportion of U.S. adults that think our political system is broken. Find the minimum sample size needed when no prior study of U.S. adults who think our political system is broken has been conducted. The manufacturer of a particular vacuum cleaner estimates that the mean length of time before the main belt needs replaced is more than 24 months. A random sample of 25 of their vacuum cleaners found a mean length of time prior to belt replacement of 26.1 months, with a standard deviation of 5.4 months. At α =.05, can you support the manufacturer s claim? 40. Can you support the claim that the mean length of time before the main belt needs replaced is more than 24 months? Why or why not? A cereal maker believes that the average American eats more than 28 boxes of cereal each year. A random sample of 73 people in the United States has a mean cereal consumption of 31.8 boxes per year, with a standard deviation of 0.7 boxes. At α =.01, can you support the cereal maker s claim? 41. Can you support the claim that the average American eats more than 28 boxes of cereal each year? Why or why not? A study of bass populations compared the weights of bass in two lakes. Fifty-four randomly selected bass from the first lake had a mean weight of 480 ounces, with a standard deviation of 60 ounces. Forty-five randomly selected bass from the second lake had a mean weight of 520 ounces with a standard deviation of 75 ounces. At α =.10, can you support the claim that the weights of bass in the two lakes are the same? 42. Can you support the claim that the weights of bass in the two lakes are the same? Why or why not? In a random sample of 7,563 students planning to major in mathematics, 3,169 were female. In a random sample of 45,897 students planning to major in business, 20,584 were female. At α =.05, can you support the claim that the proportion of women in the mathematics program is greater than the proportion of females in the business program? 43. Can you support the claim that the proportion of females in the mathematics program is greater than the proportion of females in the business program? Why or why not? In a study studying the effects of an herbal supplement on weight loss in men, 9 randomly selected men were given an herbal supplement for 21 weeks. The following measurements are for each subject s weight taken before and after the 21 week treatment period. At α =.10, can you support the claim that the supplement worked (weights went down)? Patient Before After Can you support the claim that the supplement worked (weights went down)? Why or why not? 5