Question

Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 4740 hours and standard deviation 460 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 :

Given that ,

mean = = 4740

standard deviation = = 460

a)

P(x 5000) = P((x - ) / (5000 - 4740) / 460)

= P(z 0.57)

= 0.7157

Probability = 0.7157

b)

P(Z < z ) = 10%

P(Z < z ) = 0.10

P(Z < -1.28 ) = 0.10

z = - 1.28

Using z-score formula,

X = z* +

X = -1.28 * 460 + 4740

X = 4151.2

X = 4151

4151 playing hours should the guarantee cover.