Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 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 6% of the watches it makes, how long should the guarantee period be (to the nearest month)?
  months

Answer 1

Answer:

a)

Given,

mean = 36

standard deviation = 5

To determine the percentage of total production will the company expect to replace

i.e.,

P(X < 2 yrs) = P(X < 2(12 months))

= P(X < 24)

= P(Z < x-mean/standard deviation)

substitute values given

= P(Z < (24 - 36)/5)

= P(Z < - 2.4)

= 0.0081975

Required probability = 0.01

b)

To calculate the x

P(X < x) = 0.06

P(Z < x-mean/standard deviation) = P(Z < (x - ) / ) = 0.06

Now from the z table, z critical value at 0.06 confidence level is - 1.56

(x - ) / = - 1.555

(x - 36)/5 = - 1.555

x = (-1.555*5) + 36

= 28.225

x = 28