AP Statistics Midterm Review



Name: ____________________________________ Date: _____________ Block: ____

AP Statistics Midterm Exam Review

• These are problems to assist you in practicing topics within each unit.

• It does NOT cover every topic that will be on the midterm.

• Show all work on your own paper.

• This will be worth 15 points and due on your exam day.

#1 – 4: The scores of 18 first-year private college women on the Survey of Study Habits and Attitudes

(SSHA) are:

154 109 137 115 152 140 154 178 101

103 126 126 137 165 165 129 200 148

The college also administered the test to a sample of 20 first-year men. Their scores were:

108 140 114 91 180 115 126 92 169 146

109 132 75 88 113 151 70 115 187 104

1. Make a back-to-back stemplot of the men and women’s scores.

2. Find the five-number summaries for both distributions.

3. Are there any outliers according to the outlier test? Show work.

4. Make side-by-side boxplots of the distributions. Clearly label your boxplots. Use modified boxplots if necessary.

5. Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. At a local science competition, both light bulbs lasted 750 hours. Which light bulb’s life span was better? Explain.

#6-8: A packaging machine is set to fill a cardboard box with a mean average of 16.1 ounces of cereal. Suppose the amounts per box form a normal distribution with a standard deviation of 0.04 ounces. For each problem draw the normal curve and shade in the area that represents the answer to the question.

6. What percentage of the boxes will end up with at least 1 pound (16 oz) of cereal?

7. Eighty percent of the boxes will contain more than what number of ounces?

8. The middle 90% of the boxes will be between what two weights?

9. Costs for standard veterinary services at a local animal hospital follow a normal modal with a

mean of $80 and a standard deviation of $20. Is it unusual to have a veterinary bill for $125?

Explain your answer.

#10 & 11: A medical study of heart surgery investigates the effect of a drug called a beta-blocker on the pulse rate of the patients during surgery. The pulse rate will be measured at a specific point during the operation. The investigators will use as subjects 20 patients facing heart surgery. You have a list of these patients, numbered 01 to 20, in alphabetical order.

10. Outline as an algorithm (paragraph form) or in diagram form a completely randomized

experimental design for this experiment.

11. Describe how you would simulate selecting the patients for each group.

#12 – 15: A random survey of cars in the student and faculty lots at a large university classified

the brands by where the cars were made, as seen in the table.

| | Student | Faculty |

|American | 107 | 105 |

|European | 33 | 12 |

|Asian | 55 | 47 |

12. What is the probability that a randomly selected car is a students’ car?

13. What is the probability that a car is a students and American?

14. What is the probability that a car that is driven by a faculty member is a European car?

15. Among the Asian cars, what is the probability that a faculty member drives it?

#16-19: The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking

for the right size. The box contains 4 medium, 10 large, and 6 extra large shirts. You want a

medium for you and one for your sister. Find the probability of each event described.

16. The first two you grab are the wrong size.

17. The first medium shirt you find is the third one you check.

18. The first four shirts you pick are all extra-large.

19. At least one of the first four shirts you check is a medium.

#20 & 21: To play a game, you must pay $5 for each play. There is a 10% chance you will win $5,

a 40% chance you will win $7, and a 50% chance you will win only $3.

20. What are the mean and standard deviation of your net gains?

21. You play the game twice. Assuming the plays are independent events, what are the mean and

standard deviation of your total winnings.

#22 & 23: At a certain college, 64% of the entering freshmen graduate. If we randomly selected 10 entering freshman, find the probability that:

22. Exactly 5 of the students will graduate.

23. At least 8 of the students will graduate.

#24 - 27: The loan manager at ABC bank approves 30% of all personal loan applications. Find the following probabilities:

24. If the manager received 20 applications today, what is the probability that they approve 6 of them?

25. Of those 20 applications, what is the probability that the manager approved fewer than 5 applications?

26. What is the probability that the third application on the manager’s desk was the first one they approved that day?

27. What is the probability that the manager’s first approval of the day is one of the first four applications on their desk?

28. Assume that 30% of students at a university wear contact lenses. We randomly pick 100 students. What is the approximate probability that more than a quarter of this sample wear contact lenses?

#29 - 31: The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for adults. The distribution of scores for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15.

29. What is the probability that a randomly chosen individual has a WAIS score of 110 or higher?

30 .What are the mean and standard deviation of the average WAIS scores [pic]for an SRS of 60 people?

31. What is the probability that the average WAIS score of an SRS of 60 people is 110 or higher?

Hints: #1 – 4 Chapters 2 – 5 Chapter 19: Study your notes

#5 – 9 Chapter 6

#10 &11 Chapters 11 – 13

#12-19 Chapters 14 & 15

#20 & 21 Chapter 16

#22-27 Chapter 17

#28-31 Chapter 18

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