Binomial Random Variables Answers

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?

Consider the given probability histogram of a binomial random variable.

A certain airline has a 90% probability that its flights are on time. Fifteen of this airline’s flights leave the local airport each day. Let X represent the number of flights that are on time each day. Assuming flights are on time independently of one another, what is the shape of the probability histogram of X?

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?

In a family of five children, there is a 25% chance that each individual child has freckles. Children inherit freckles independently of one another. Let X represent the number of children in this family with freckles. What are the mean and standard deviation of X?

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?

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?

According to a website, one out of five adults will make an online purchase in any given week. A survey asked 20 randomly selected adults if they had made an online purchase within the past week. Let X represent the number of adults who had made an online purchase within the past week.What is the shape of the probability histogram of X?

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?

A produce manufacturer fills bags of baby carrots by weight. Each bag is supposed to have 12 ounces of baby carrots. Unfortunately, 3% of the baby carrots are discolored. Let X represent the number of discolored baby carrots in a bag.Are the conditions for a binomial setting in this scenario met?