Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 95% confidence interval for the population mean of all bulbs produced by this firm.

		764.99 < µ < 795.008
		768.02 < µ < 791.98
		700.30 < µ < 859.70
		765.69 < µ < 794.31

Answer 1

solution:

Solution :

Given that,

= 780

= 40

n = 30

Solution :

Given that,

=

=

n =

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96* (40 / 30)

= 14.31

At 95% confidence interval mean is,

- E < < + E

780-14.31 < < 780+14.31

765.69 < µ < 794.31

(, )