Question 1

Suppose we flip a coin 10 times. The probability that heads occurs exactly the same number of times as tails on the 10 flips is:

Accepted Answer

A) 0.1667. 
B) 0.2461. 
C) 0.3125. 
D) 0.5. 
A) 0.1667. 
B) 0.2461. 
C) 0.3125. 
D) 0.5. B

Question 2

A college basketball player makes 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 of these attempts?

Accepted Answer

A) about 0.9 
B) about 0.7 
C) about 0.3 
D) about 0.006 
A) about 0.9 
B) about 0.7 
C) about 0.3 
D) about 0.006 D

Question 3

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The mean of X is:

Accepted Answer

A) 0.4. 
B) 0.8. 
C) 1.2. 
D) 1.6. 
A) 0.4. 
B) 0.8. 
C) 1.2. 
D) 1.6. B

Question 4

A local veterinary clinic recently had 25 horses admitted from the same barn. It was determined that most cases of West Nile virus infection in the group of 25 horses were caused by infection by another horse. In this case, modeling the number of cases diagnosed with a binomial distribution is not appropriate because:

Accepted Answer

A) the success on different trials needs to be mutually exclusive and this is not the case here. 
B) the success on individual trials needs to be independent. 
C) the success on individual trials needs to be positive. 
D) n = 25 is a very small sample. 
A) the success on different trials needs to be mutually exclusive and this is not the case here. 
B) the success on individual trials needs to be independent. 
C) the success on individual trials needs to be positive. 
D) n = 25 is a very small sample.

Question 5

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The standard deviation of X is:

Accepted Answer

A) 0.71 
B) 0.768. 
C) 0.8. 
D) 0.88. 
A) 0.71 
B) 0.768. 
C) 0.8. 
D) 0.88.

Question 6

Suppose a flu epidemic is sweeping a campus and many students are sick. Student health services finds that 30% of students are ill. A nurse samples a dormitory with 30 students and wants to calculate the probability that at least 10 students are sick. Which of the following statements is false?

Accepted Answer

A) The binomial distribution cannot be used in this example, because the probability that 1 student is sick is not independent of another student in the dorm also being sick. 
B) The Normal approximation to the binomial cannot be used, because the binomial distribution is not an appropriate model. 
C) The Normal approximation to the binomial could not be used, even if the binomial were an appropriate model, because np = 30 × 0.3 = 9 and this violates one criterion for using the Normal approximation. 
D) The binomial distribution can be used here, because our variable of interest is a finite count with minimum 0 and maximum 30. 
A) The binomial distribution cannot be used in this example, because the probability that 1 student is sick is not independent of another student in the dorm also being sick. 
B) The Normal approximation to the binomial cannot be used, because the binomial distribution is not an appropriate model. 
C) The Normal approximation to the binomial could not be used, even if the binomial were an appropriate model, because np = 30 × 0.3 = 9 and this violates one criterion for using the Normal approximation. 
D) The binomial distribution can be used here, because our variable of interest is a finite count with minimum 0 and maximum 30.

Question 7

A college basketball player makes 70% of his free throws. At the end of a game, his team is losing by two points. He is fouled attempting a three-point shot and is awarded three free throws. Assuming each free throw is independent, what is the probability that he makes at least two of the free throws?

Accepted Answer

A) 0.784 
B) 0.7 
C) 0.441 
D) 0.216 
A) 0.784 
B) 0.7 
C) 0.441 
D) 0.216

Question 8

A study investigated the use of social media by freshman. One question asked if the person answering ever stayed up late to chat with friends and ended up sleep deprived. It was thought that at least 80% of all people of freshman age would stay up late. If the study sampled 400 students, what is the mean number of students staying up late in random samples of n = 400 in the freshman population?

Accepted Answer

A) 80 
B) 160 
C) 240 
D) 320 
A) 80 
B) 160 
C) 240 
D) 320

Question 9

A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes exactly three of his next four free throws is:

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
A)    . 
B)    . 
C)    . 
D)    .

Question 10

A study investigated the use of social media by freshman. One question asked if the person answering ever stayed up late to chat with friends and ended up sleep deprived. It was thought that at least 80% of all people of freshman age would stay up late. If the study sampled 400 students, which of the following statements is true?

Accepted Answer

A) The number of students in the sample who stay up late follows a binomial distribution with F1F1F1S1F1F1F10 = 320 and variance F1F1F1S1F1F1F102 = 64. 
B) The number of students in the sample who stay up late can be approximated by a Normal distribution with mean F1F1F1S1F1F1F10 = 320 and variance F1F1F1S1F1F1F102 = 64. 
C) The number of students in the sample who stay up late can be approximated by a Normal distribution with mean F1F1F1S1F1F1F10 = 320 and standard deviation F1F1F1S1F1F1F10 = 8. 
D) All of the answer options are correct. 
A) The number of students in the sample who stay up late follows a binomial distribution with F1F1F1S1F1F1F10 = 320 and variance F1F1F1S1F1F1F102 = 64. 
B) The number of students in the sample who stay up late can be approximated by a Normal distribution with mean F1F1F1S1F1F1F10 = 320 and variance F1F1F1S1F1F1F102 = 64. 
C) The number of students in the sample who stay up late can be approximated by a Normal distribution with mean F1F1F1S1F1F1F10 = 320 and standard deviation F1F1F1S1F1F1F10 = 8. 
D) All of the answer options are correct.

Question 11

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability a randomly selected horse among the 10 new admits has West Nile virus?

Accepted Answer

A) 0.1 
B) 0.5 
C) 0.15 
D) 0.9 
A) 0.1 
B) 0.5 
C) 0.15 
D) 0.9

Question 12

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The probability that X is at least 1 is:

Accepted Answer

A) 0.22. 
B) 0.44. 
C) 0.56. 
D) 0.77. 
A) 0.22. 
B) 0.44. 
C) 0.56. 
D) 0.77.

Question 13

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on seven of eight incorrectly answered problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, the guess for one problem is independent of the guess for the other problems. The probability of getting agreement on seven or more out of eight questions is:

Accepted Answer

A) 0.9996. 
B) 0.0004. 
C) 0.25. 
D) None of the answer options is correct. 
A) 0.9996. 
B) 0.0004. 
C) 0.25. 
D) None of the answer options is correct.

Question 14

Opinion polls find that 20% of American adults claim they never have time to relax. Suppose you take a random sample of 200 American adults, and you count the number X in your sample that claim they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is:

Accepted Answer

A) less than 0.0001. 
B) about 0.962. 
C) about 0.2. 
D) about 0.038. 
A) less than 0.0001. 
B) about 0.962. 
C) about 0.2. 
D) about 0.038.

Question 15

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. Last month, 100 horses were admitted and 20 of them had been infected with West Nile virus. The probability of seeing 20 or more horses with West Nile virus was calculated based on a Normal distribution with F1F1F1S1F1F1F10 = 15 and F1F1F1S1F1F1F10 = 12.75. Which of the following statements is true?

Accepted Answer

A) Using the Normal approximation to the binomial distribution is justified, because X = 20 > 10. 
B) Using the Normal approximation to the binomial distribution is justified, because n is large and exact calculations are too tedious. 
C) Using the Normal approximation to the binomial distribution is justified, because np = 15 and n(1 - p)= 85. 
D) All of the answer options are correct. 
A) Using the Normal approximation to the binomial distribution is justified, because X = 20 > 10. 
B) Using the Normal approximation to the binomial distribution is justified, because n is large and exact calculations are too tedious. 
C) Using the Normal approximation to the binomial distribution is justified, because np = 15 and n(1 - p)= 85. 
D) All of the answer options are correct.

Question 16

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on seven of eight incorrectly answered problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, the guess for one problem is independent of the guess for the other problems. The number of guesses by student B that agree with those of student A has mean and variance given by:

Accepted Answer

A) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F102 = 1.5. 
B) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F102 = 1.52. 
C) F1F1F1S1F1F1F10 = 4 and F1F1F1S1F1F1F102 = 1.5. 
D) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F10 = 1.5. 
A) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F102 = 1.5. 
B) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F102 = 1.52. 
C) F1F1F1S1F1F1F10 = 4 and F1F1F1S1F1F1F102 = 1.5. 
D) F1F1F1S1F1F1F10 = 2 and F1F1F1S1F1F1F10 = 1.5.

Question 17

A group of economists surveys consumers of smartphones to see which devices consumers prefer. The question asked of shoppers is whether they are purchasing a Windows device or another type. The economists count the number of shoppers expressing preference for a Windows device. The survey samples about 50 shoppers from among several million. Which of the following criteria is violated regarding a binomial model?

Accepted Answer

A) There are more than two possibilities for smartphones, and the binomial allows only two categories: success and failure. 
B) This is sampling without replacement and, therefore, the observations are dependent despite the large population. 
C) The binomial has to be a finite count between zero and some fixed upper value. 
D) None of the criteria listed is violated. 
A) There are more than two possibilities for smartphones, and the binomial allows only two categories: success and failure. 
B) This is sampling without replacement and, therefore, the observations are dependent despite the large population. 
C) The binomial has to be a finite count between zero and some fixed upper value. 
D) None of the criteria listed is violated.

Question 18

A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false?

Accepted Answer

A) The approximation requires np F1F1F1S1F1F1F10 10 and n(1 - p)F1F1F1S1F1F1F10 10. 
B) The sample size here is too small to use the Normal approximation to the binomial. 
C) The approximation requires np F1F1F1S1F1F1F10 30. 
D) The Normal approximation works better if the success probability p is close to p = 0.5. 
A) The approximation requires np F1F1F1S1F1F1F10 10 and n(1 - p)F1F1F1S1F1F1F10 10. 
B) The sample size here is too small to use the Normal approximation to the binomial. 
C) The approximation requires np F1F1F1S1F1F1F10 30. 
D) The Normal approximation works better if the success probability p is close to p = 0.5.

Question 19

A hobby gardener planted 20 rose bushes, 8 of which produced red roses and the other 12 produced white roses. The gardener randomly samples 5 rose bushes to be treated with a new plant food. He wants to calculate the probability that only white rose bushes get selected. Which of the following distributions can he use to calculate this probability?

Accepted Answer

A) the Normal distribution 
B) the binomial distribution 
C) the Normal approximation to the binomial distribution 
D) None of the answer options is correct. 
A) the Normal distribution 
B) the binomial distribution 
C) the Normal approximation to the binomial distribution 
D) None of the answer options is correct.

Question 20

Suppose we toss a fair coin repeatedly. We continue to do this until a tail is observed. Let X be the number of tosses required. Then X has:

Accepted Answer

A) a binomial distribution, with mean 0.5. 
B) a binomial distribution, with mean 2. 
C) a binomial distribution, with variance 0.707. 
D) None of the answer options is correct. 
A) a binomial distribution, with mean 0.5. 
B) a binomial distribution, with mean 2. 
C) a binomial distribution, with variance 0.707. 
D) None of the answer options is correct.

Suppose we flip a coin 10 times. The probability that heads occurs exactly the same number of times as tails on the 10 flips is:

A college basketball player makes 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 of these attempts?

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The mean of X is:

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The standard deviation of X is:

Suppose a flu epidemic is sweeping a campus and many students are sick. Student health services finds that 30% of students are ill. A nurse samples a dormitory with 30 students and wants to calculate the probability that at least 10 students are sick. Which of the following statements is false?

A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes exactly three of his next four free throws is:

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability a randomly selected horse among the 10 new admits has West Nile virus?

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The probability that X is at least 1 is:

Opinion polls find that 20% of American adults claim they never have time to relax. Suppose you take a random sample of 200 American adults, and you count the number X in your sample that claim they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is:

Suppose we toss a fair coin repeatedly. We continue to do this until a tail is observed. Let X be the number of tosses required. Then X has:

Getting Started

Picturing Distributions With Graphs

Describing Distributions With Numbers

The Normal Distributions

Scatterplots and Correlation

Two-Way Tables

Producing Data- Sampling

Producing Data- Experiments

Data Ethics

Introducing Probability

General Rules of Probability

Inference for Regression

One-Way Analysis of Variance- Comparing Several Means

Nonparametric Tests

More on Analysis of Variance

Filters

Exam 12: Binomial Distributions

Suppose we flip a coin 10 times. The probability that heads occurs exactly the same number of times as tails on the 10 flips is:

A college basketball player makes 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 of these attempts?

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The mean of X is:

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The standard deviation of X is:

Suppose a flu epidemic is sweeping a campus and many students are sick. Student health services finds that 30% of students are ill. A nurse samples a dormitory with 30 students and wants to calculate the probability that at least 10 students are sick. Which of the following statements is false?

A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes exactly three of his next four free throws is:

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability a randomly selected horse among the 10 new admits has West Nile virus?

At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The probability that X is at least 1 is:

Opinion polls find that 20% of American adults claim they never have time to relax. Suppose you take a random sample of 200 American adults, and you count the number X in your sample that claim they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is:

Suppose we toss a fair coin repeatedly. We continue to do this until a tail is observed. Let X be the number of tosses required. Then X has:

Getting Started

Picturing Distributions With Graphs

Describing Distributions With Numbers

The Normal Distributions

Scatterplots and Correlation

Two-Way Tables

Producing Data- Sampling

Producing Data- Experiments

Data Ethics

Introducing Probability

General Rules of Probability

Inference for Regression

One-Way Analysis of Variance- Comparing Several Means

Nonparametric Tests

More on Analysis of Variance

Filters