A battery manufacturer claims that the lifetime of certain type of battery is normal with population mean of 50 hours and a standard deviation of 4 hours.. Let X( has bar on on top) be the mean lifetime of a random sample of 100 of these batteries.

a) What is the expected value of X ? (p.s x has bar on top)

b) What is the standard deviation of X? (p.s x has bar on top)

c) If the manfacturer's claim is true then what is the approximate probability P ( X < 49.1)?

d) If the manufacturer's claim is true then what is the approximate probability P ( X < 49.1)? (p.s x has bar on top)

e) If K is a constant such that P ( X > K ) = .09 then find K.

f) If K is a constant such that P ( X > K ) =.09 then find K. (p.s x has bar on top)