Question

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? skewed left skewed right approximately uniform approximately symmetric

Answer 1

d. approximately symmetric

Explanation:

Answer 2

Since each customer's decision to make a purchase is independent of other customers' decisions and there is a fixed probability of 0.52 for each customer to make a purchase, we can model the number of customers who make a purchase, X, using a binomial distribution.

The probability histogram of a binomial distribution is approximately symmetric when the probability of success (p) is close to 0.5, and becomes more skewed as p gets closer to 0 or 1. In this case, p = 0.52, which is close to 0.5, so the probability histogram of X is approximately symmetric.

Therefore, the answer is: approximately symmetric.

Explanation: