Question

Fluorescent lighbulbs have lifetimes that follow a normal distribution, with an average life of 1,725 days and a standard deviation of 1,462 hours. In the production process the manufacturer draws random samples of 215 lightbulbs and determines the mean lifetime of the sample.

What would be the standard deviation, in hours, of the sampling distribution?

Std. dev. of sample means (1 decimal place):

Answer 1

Solution :

Given that ,

mean = $\mu$ = 1725

standard deviation = $\sigma$ = 1462

n = 215

sample distribution of sample mean is ,

$\mu$
T
= $\mu$

$\mu$ = 1725

T

sampling distribution of standard deviation

$\sigma$
T
=$\sigma$  / $\sqrt$ n = 1462 / $\sqrt$ 215=99.7076

$\sigma$ = 99.7

T