3 marks) Question Two (a) The length of life of a certain type of automatic wash

Question

3 marks) Question Two (a) The length of life of a certain type of automatic washer is normally distributed, with a mean of 3.1 years and variance 1.44 years. If this type of washer is guaranteed for I year, what fraction of original sales will require replacement? 3 marks) (b) Hair dryers and blowers have recently become very popular as a result of longer hairstyles. To ascertain the quality of various hair blowers on the market, a well-known testing service conducted an intensive study of these products. As part of their study it was reported that the length of life of a certain product tested was normally distributed, with a mean life of 1200 hours and a standard deviation of 100 hours. How long should the guarantee time be ifthe manufacturer of the product wants to replace only 10% of the hair blowers sold? (3 marks)

Explanation / Answer

Solution

Q2a

Let X = life of automatic washer in years.

Given X ~ N(3.1, 1.22)

Given the guarantee is one year, sales will require replacement if it fails within one year. So, fraction of sales requiring replacement

= P(X < 1)

= 0.04 or 4% [using Excel Function of Normal Distribution] ANSWER

Q2b

Let Y = life of hair dryer in hours.

Given Y ~ N(1200, 1002)

Let the guarantee period be t years. Then there will be sales return if the dryer fails within t year. So, probability of sales return

= P(Y < t)

We want this probability to be 0.1 (10%)

So, P(Y < t) = 0.1

=> t = 1071.845 hours [using Excel Function of Normal Distribution] or

1072 hours ANSWER

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