Question

A factory makes components used in jet engines, including reinforced steel washers. The washers are required to have a very precise thickness. The thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. A technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. What is the probability that x¯<1.57 ?

Answer 1

= 1.59

= 0.042

n = 20

SE = /

= 0.042/

= 0.009391

To find P( < 1.57):

Z = (1.57 - 1.59)/0.009391

= - 2.1296

Table of Area Under Standard Normal Curve gives area = 0.4834

So,

P(<1.57) = 0.5 - 0.4834 = 0.0166

So,

Answer is:

0.0166