Binomial Random Variables Answers

The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament, and the games are played independently of one another. Let X represent the number of games the team might win in this tournament. What are the mean and standard deviation of X?

A clothing store manager notices that when any one customer comes into the store, there is a 52% chance they will make a purchase. She also notices that one customer’s decision to make a purchase is independent of other customers’ decisions. Suppose one Friday, 75 customers come into this store. Let X represent the number of customers who make a purchase.What is the shape of the probability histogram of X?

Tropical islands have many rainstorms during the afternoon heat. One particular tropical island has a 79% chance of a rainstorm on any given afternoon. Abraham is planning a weeklong stay on this tropical island. Let X represent the number of days there is an afternoon tropical storm that week. What are the mean and standard deviation of X?

Consider the given probability histogram of a binomial random variable.

Ian shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the number of aces he observes.Have the conditions for a binomial setting been met for this scenario?

A fair coin is flipped three times, and the number of times it comes up "heads” is recorded.Have the conditions for a binomial setting been met for this scenario?

A spinner is divided into six equal-sized sectors labeled 1 through 6. Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun. What are the mean and standard deviation of X?

The probability of an archer hitting her target is 83%. Suppose she has 20 shots to take, and each shot is independent of the others. Let X represent the number of targets hit. What is the mean of X?

A coin is weighted so that the probability of getting heads is . Suppose you toss this coin 15 times. Let X represent the number of heads. What are the mean and standard deviation of X?

There are 10 multiple-choice questions on a math quiz. Each question has four answer choices with one correct answer. Let X represent the number of questions answered correctly for a student who is randomly guessing each answer choice.Have the conditions for a binomial setting been met for this scenario?