Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes 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? (Round your answer to two decimal places.)


(b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)?

Answer 1

P(z<Z) table :

a.

x = life

P(replace)

= P(x<=24 months) :

30.85 % of total production the company will expect to replace

b.

P(x< k months) = 0.12

P(z<Z) = 0.12

Z = -1.17 {from table}

k = 26 + (-1.17)*4

= 21.32 = 21 (to nearest month)

therefore,

the guarantee period should be 21 months

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