Answer to Question #198963 in Statistics and Probability for Laine

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

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{1400-1500}{500/\sqrt{40}}=-1.26$

a)

$(\overline{x}>1400)=1-P(z<-1.26)=1-0.10565=0.89435$

b)

$(\overline{x}<1400)=P(z<-1.26)=0.10565$