Question

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 9.8 inches, and standard deviation of 1.6 inches. If 48 items are chosen at random, what is the probability that their mean length is greater than 9.2 inches

Answer 1

0.6462

Explanation:

Given that

Mean (m) = 9.8

Standard deviation (s) = 1.6

Probability that mean length is greater than 9.2

Z = (x - m) / s

Z = (9.2 - 9.8) / 1.6

Z = - 0.6 / 1.6

Zscore = - 0.375 = - 0.375

P(Z >- 0.375) = 1 - P(Z < - 0.375) ;

P(Z < - 0.375) = 0.3538

1 - P(Z < - 0.38) = 1 - 0.3538 = 0.6462