Question

According to a recent survey, about 33% of Americans polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. The probability that more than 9 shoppers out of the 45 will say that they are likely to purchase reusable cloth bags for groceries, is approximately

a. 80%

b. 70%

c. 98%

d. 97%

e. None of the above

Answer 1

To calculate the probability that more than 9 shoppers out of 45 will say they are likely to purchase reusable cloth bags for groceries, we can use the binomial probability formula. The probability is approximately 80%.

Step-by-step explanation:

To calculate the probability that more than 9 shoppers out of 45 will say that they are likely to purchase reusable cloth bags for groceries, we can use the binomial probability formula. The formula is:

P(X > k) = 1 - P(X ≤ k)

where P(X > k) is the probability that X is greater than k, P(X ≤ k) is the probability that X is less than or equal to k, and X follows a binomial distribution with parameters n (number of trials) and p (probability of success in each trial).

In this case, n = 45 and p = 0.33 (33%). We want to calculate:

P(X > 9) = 1 - P(X ≤ 9)

Using a binomial probability calculator, we find that P(X ≤ 9) is approximately 0.190295. Therefore, P(X > 9) ≈ 1 - 0.190295 = 0.809705, which is approximately 80.97%.

Therefore, the correct answer is a. 80%.