If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL

Question

8. Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (mL) and standard deviation 1.6. If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL

Answer 1

M = mean = 102.1

mu = 101.5

sigma = 1.6

n = 36

z = (102.1 - 101.5)/(1.6/sqrt(36)) = 2.25

P(M < 102.1) = P(z < 2.25) = 0.9878