Question

A company manufactures light bulbs. These light bulbs have a length of life that is normally distributed with a known standard deviation of 40 hours. If a sample of 36 light bulbs has an average life of 780 hours, find the 95 percent confidence interval for the population mean of all light bulbs manufactured by this company.

Answer 1

Solution

Given that,

= 780

=40

n = 36

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 * (40 / 36 )

= 13.07

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

- E < < + E

780 - 13.07< < 780 + 13.07

766.93 < < 793.07

(766.93 , 793.07)