Question

A metal part used in cars is manufactured with a mean diameter of 2.565 cm and a standard deviation of 0.008 cm. Knowing the diameter is Normally distributed, find the probability that a random sample of n=9 sections of a metal part will have a sample mean diameter greater than 2.560cm and less than 2.570 cm.

Answer 1

= 2.565

= 0.008

n = 9

SE = /

= 0.008/ = 0.0027

To find P(2.56 < < 2.57):

Case 1: For from 2.565 to mid value:

Z = (2.56 -2.565)/0.0027 = - 1.8519

Table of Area Under Standard Normal Curve gives area = 0.4678

Case 2: For from mid value to 2.57:
Z = (2.57 - 2.565)/0.0027 = 1.8519

Table gives area = 0.4678

So,

P(2.56 < < 2.57) =2 X 0.4678 = 0.9356