Question

A manufacturer knows that their items have a normally distributed length, with a mean of 11.5 inches, and a standard deviation of 0.5 inches. If 19 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?

Answer 1

Solution :

Given that ,

mean = = 11.5

standard deviation = = 0.5

= / n = 0.5 / 19 = 0.1147

P( < 11.2) = P(( - ) / < (11.2 - 11.5) / 0.1147)   

P(z < -2.6155)

= 0.0045

Probability = 0.0045