5. Binomial Distribution & Discrete Random Variables

A basketball player normally has a 70% chance of making a free throw. The player shoots until finally making a basket, where $x$ is the number of shots they take. Is this a binomial experiment?

You take a 6-question quiz with True/False questions. What is the probability of getting all 6 questions correct by simply guessing?

National surveys indicate that 36% of people have been in a car accident in the last 5 years. If you randomly sample 10 people, how likely is that exactly 4 have had an accident in the last 5 years?

Based on historical weather data in a certain city, about 62% of the days are cloudy. Find the mean, standard deviation, and variance for the number of cloudy days in a 30-day month.

Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 4 is a significantly high number of drivers who say that they text while driving.

Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Using Probabilities for Significant Events

a. Find the probability of getting exactly 3 drivers who say that they text while driving.

Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.

Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.

b. Beginning with WWC, make a complete list of the different possible arrangements of two wrong answers and one correct answer, and then find the probability for each entry in the list.

Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.

Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.

c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?