Question

GE, a company that makes light bulbs claims that its bulbs have a mean life of 800 hours with a standard deviation of 32 hours. Show all work

a)If you buy a four-pack of bulbs, what is the probability that the mean life will be 775 to 850 hours for that four-pack ?

b)If you buy a case of 40 bulbs, what is the probability that the mean lifewill be 775 to 850 hours for the entire case?

answers accurate to four dsecimal places

Answer 1

Given,

= 800, = 32

The central limit theorem is

P( < x) = P( Z < x - / )

a)

For n = 4

P( 775 < < 850) = P( < 850) - P( < 775)

= P( Z < 850 - 800 / 32 / sqrt(4) ) - P( Z < 775 - 800 / 32 / sqrt(4) )

= P( Z < 3.125) - P( Z < -1.5625)

= 0.9991 - 0.0591

= 0.9400

b)

For n = 40

P( 775 < < 850) = P( < 850) - P( < 775)

= P( Z < 850 - 800 / 32 / sqrt(40) ) - P( Z < 775 - 800 / 32 / sqrt(40) )

= P( Z < 9.8821) - P( Z < -4.9411)

= 1 - ( 1 - 1)

= 1.0000