In: Statistics and Probability
Problem Page
The lifetime of a certain brand of electric light bulb is known to have a standard deviation of
48
hours. Suppose that a random sample of
50
bulbs of this brand has a mean lifetime of
480
hours. Find a
99%
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.
Solution :
Given that,
= 480
= 48
n = 50
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z/2* ( /n)
= 2.576 * (48 / 50)
= 17.5
At 99% confidence interval estimate of the population mean is,
- E < < + E
480 - 17.5 < < 480 + 17.5
462.5 < < 497.5
(462.5 , 497.5)