1 8.Guarantee: Disc Players Future Electronics makes compact disc players. Its r

Question

1 8.Guarantee: Disc Players Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 5000 hours and standard deviation 450 hours. (a) Find the probability that the laser beam device will wear out in 5000 hours or less. (b) Inverse Normal Distribution Future Electronics wants to place a guarantee on the players so that no more than 5% fail during the guarantee period. Because the laser pickup is the part most likely to wear out first, the guar- antee period will be based on the life of the laser beam device. How many playing hours should the guarantee cover? (Round to the next playing hour.)

Explanation / Answer

Solution:

Part a

We are given that the life of compact disc players follows normal distribution.

Mean = 5000 hours

SD = 450 hours

We have to find P(X5000)

P(X5000) = P(X<5000) (it is a continuous distribution.)

Z = (X – mean) / SD

Z = (5000 – 5000) / 450

Z = 0

P(Z<0) = P(X5000) = 0.5000 (By using z-table)

Required probability = 0.5000

Part b

Here, we have to find the value X for which probability is 5%.

X = Mean + Z*SD

Z for 5% is given as -1.645.

X = 5000 – 1.645*450

X = 4259.815868

Required Answer = 4260 hours

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