Question

A manufacturer knows that their items have a normally distributed length, with a mean of 10.2 inches, and standard deviation of 1.8 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 9.8 inche

Answer 1

P [ X ≤ 9.8 ] = 0.1335

Explanation:

P [ X ≤ 9.8 ] = [ ( 9.8 - 10.2 )/1.8√25 ]

P [ X ≤ 9.8 ] = - 0.4*5/1.8

P [ X ≤ 9.8 ] = - 2 / 1.8

P [ X ≤ 9.8 ] = - 1.11

From z- table we get: α = 0.1335

P [ X ≤ 9.8 ] = 0.1335 or P [ X ≤ 9.8 ] = 0.1335