Question

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.8% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine.(b) Assuming his suspicion that 9.8% of his customers buy a magazine is correct, what is the probability that exactly 2 out of the first 11 customers buy a magazine? Give your answer as a decimal number rounded to two digits.(c) What is the expected number of customers from this sample that will buy a magazine?

Answer 1

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of his customers that buy a magazine. This is a binomial distribution since the outcomes are two ways. It is either a selected customer buys a magazine or he doesn't. The probability of success, p = 9.8/100 = 0.098

The probability of failure, q would be 1 - p = 1 - 0.098 = 0.902

b We want to determine P(x = 2)

n = 11

From the binomial distribution calculator,

P(x = 2) = 0.21

c) the expected number of customers from this sample that will buy a magazine is same as the mean.

mean = np

mean = 11 × 0.098 = 1.08