Watches Accrotime is a manufacturer of quartz crystal watches. Accrotime researc

Question

Watches Accrotime is a manufacturer of quartz crystal watches. Accrotime

researchers have shown that the watches have an average life of 28 months before certain

electronic components deteriorate, causing the watch to become unreliable. The standard

deviation of watch lifetimes is 5 months, and the distribution is normal.

a.) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase,

what percentage of total production will the company expect to replace?

b.) Inverse Normal Distribution If Accrotime does not want to make refunds on more than

8% of the watches it makes, how long should the guarantee period be (to the nearest

month)?

Explanation / Answer

mean = 28 , s = 5

a)

P (X<24)

z = ( x- mean) / s

= (24 - 28) / 5

= -0.8

Now, we need to find P(Z < -0.8)

P(X < 24) = P(Z < -0.8) = 0.2119 = 21%

b) z value for 8% = -0.405

x bar = mean+ z *s

= 28 - 0.405 * 5

= 25.975 = 26 months

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