Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers hav

Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have determined that the watches have an average life of 79 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 11 months, and the distribution of lifetimes is normal.

a. If Accrotime guarantees a full refund on watches for 6 years (72 months) after purchase, what percentage of total production will the company expect to replace?

b. If Accrotime doesn’t want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month).

Explanation / Answer

a) (X < 72)

= ((X - mean)/sd < (72 - mean)/sd)

= (Z < (72 - 79)/11)

= P(Z < -0.64)

= 0.2611

= 26.11%

b) P(X < x) = 0.06

or, P((X - mean)/sd < (x - mean)/sd) = 0.06

or, P(Z < (x - 79)/11) = 0.06

or, (x - 79)/11 = -1.55

or, x = -1.55 * 11 + 79

or, x = 61.95

or, x = 62

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