Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with an unknown standard deviation. If a sample of 30 bulbs has an average life of 780 hours and a sample standard deviation of 50 hours, find a 95% confidence interval for the population mean of all bulbs produced by this firm.

		761.33 < µ < 798.67
		764.49 < µ < 795.91
		765.07 < µ < 794.93
		768.02 < µ < 791.98

Answer 1

Solution :

Given that,

= 780

s = 50

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,29 =2.045

Margin of error = E = t_/2,df * (s /n)

= 2.045 * (50 / 30) = 18.668

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

- E < < + E

780 -18.668 < < 780 +18.668

761.33 < < 798.67