Question

The lifetime of a certain brand of electric light bulb is known to have a standard deviation of

51 hours. Suppose that a random sample of 70 bulbs of this brand has a mean lifetime of 493 hours. Find a 95% confidence interval for the true mean lifetime of all light bulbs of this brand. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the 95% confidence interval?
What is the upper limit of the 95% confidence interval?

Answer 1

Solution :

Given that,

= 493

= 51

n = 70

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 * (51 / 70)

= 11.948

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

- E < < + E

493 - 11.948 < < 493 +11.948

481.1< < 504.9

(lower limit = 481.1 upper limit =  504.9 )