A convenience store estimates that 25% of its customers come in to buy milk. What is the probability that out of the next 200 customers, 60 or fewer will buy milk?
A) 0.4484
B) 0.9484
C) 0.0516
D) Almost no chance
E) 0.0505

Question

Quizplus · Accepted Answer

The problem can be modeled using a binomial distribution with n = 200 and p = 0.25. To find the probability that 60 or fewer customers buy milk, we calculate P(X ≤ 60). Using a normal approximation to the binomial distribution, the mean μ = np = 50 and the standard deviation σ = √(np(1-p)) ≈ 6.1237. The z-score for X = 60 is (60-50)/6.1237 ≈ 1.632. Using standard normal distribution tables or a calculator, P(X ≤ 60) ≈ 0.0516.

A Convenience Store Estimates That 25% of Its Customers Come