Question

Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 5020 hours and standard deviation 450 hours.

(a) Find the probability that the laser beam device will wear out in 5000 hours or less. (Round your answer to four decimal places.)

_______


(b) Future Electronics wants to place a guarantee on the players so that no more than 10% fail during the guarantee period. Because the laser pickup is the part most likely to wear out first, the guarantee period will be based on the life of the laser beam device. How many playing hours should the guarantee cover? (Round your answer down to the nearest hour.)

_____hr

Answer 1

Solution :

a) mean = = 5020

standard deviation = = 450

P(x 5000)

= P[(x - ) / (5000 - 5020) /450 ]

= P(z -0.04)  

= 0.4840

probability = 0.4840

b) 10%

P(Z z ) = 0 .10

z = -1.282

Using z-score formula,

x = z * +

x = -1.28 * 450+ 5020

x = 444 hous.