Question

A LED company claims that the average life of the LED light bulbs it

manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random

sample of 40 bulbs is chosen, what is the probability that the sample mean will be:

a. greater than 1, 400 hours?

b. less than 1, 400 hours?

Answer 1

Population mean $\mu=1,500$

Standard deviation $\sigma=500$

Sample size $n=40$

$Z=\dfrac{\bar x-\mu}{\sigma/\sqrt n}=\dfrac{1400-1500}{500/\sqrt{40}}$

$Z=-1.26$

(a) $\bar x>1400$

$=1−P(z<−1.26)$

$=1−0.10565$

$=0.89435$

(b) $\bar x<1400$

$=P(z<−1.26)$

$=0.10565$