Question

A manufacturer produces piston rings for an automobile engine. It is known that the ring diameter is normally distributed with σ = 0.001 millimeters. When a random sample of 16 rings is collected, the sample mean of the rings’ diameters is of x- = 74.036 millimeters.

a.) In order to find a confidence interval for the true mean piston ring diameter, which distribution table would you use?

b.) Find the lower bound of a 95% confidence interval for the mean piston ring diameter.

Answer 1

Solution

Given that,

a ) Using standard normal table

b ) = 74.036

= 0.001

n = 16

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z/2* (/n)

= 1.960 * (0.001 / 16 )

= 0.0005

At 95% confidence interval estimate of the population mean is,

- E < < + E

74.036- 0.0005 < < 74.036+ 0.0005

74.0355< < 74.0365

(59.8 , 65.2)