5
QuizMultiple Choice

Binomial Random Variables

Question 5 • College Prep Math B - IC26

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?

Answer
A
skewed left
B
skewed right
C
approximately uniform
D
approximately symmetric

Explanation

X follows a binomial distribution with 75 independent customers and purchase probability 0.52. Since 0.52 is close to 0.50, the probabilities of values on either side of the center are nearly balanced, so the histogram is approximately symmetric. Its center is about 75 × 0.52 = 39 purchases.

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