Answer to Question #329787 in Statistics and Probability for John

Question

Aneco an Electrical Company claims that the average lifeof the bulbs it manufactures is 1,200 hours with a standard deviation of 250 hours. If random sample of 100 bulbs is chosen, what is the probability that the sample mean will be.

Answer 1

$a) P(x>1150) = (x-\mu)/\sigma/\sqrt n = (1150-1200)/250/\sqrt {100} = 0.02275$

$1 - 0.02275 = 0.97725$

97.73%

$b)$$P(x<1250) = (x-\mu)/\sigma/\sqrt n = (1250-1200)/250/\sqrt {100} = 0.97725$

$1-0.97725 = 0.02275$

2.28%

c) 0.97725 - 0.02275 = 0.9545

95.45%