Question

Accrotime is a manufacturer of watches. Accrotime researchers have shown that 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.

1) If Accrotime guarantees a full refund of any defective watch for 1.5 years after the purchase, what percentage of total production will the company expect to replace? Write your answer as a percentage rounded to 1 decimal place.

2)  If Accrotime does not want to make refunds on more than 15% of the watches it makes, how long should the guarantee be (to the nearest month)?

Answer 1

Solution :

Given that ,

1) 1.5 years = 18 months

P(x < 18)

= P[(x - ) / < (18 - 28) / 5]

= P(z < -2.00)

Using z table,

= 0.0228

percentage = 2.28%

2) Using standard normal table,

P(Z < z) = 15%

= P(Z < -1.036 ) = 0.15

z = -1.036

Using z-score formula,

x = z * +

x = -1.036 * 5 + 28

x = 22.82

x = 23 months.

x =