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.

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?

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?