Question

If the life in years of a television set is normally distributed with a mean of 36 years and a standard deviation of 8 years what should be the guarantee period if the company wants less than 3% of the television sets to fail while under warranty

Answer 1

The company should guarantee a lifetime of less than equal to 20.95 years so that less than 3% of the television sets fail while under warranty.

Explanation:

We are given the following information in the question:

Mean, μ = 36 years

Standard Deviation, σ = 8 years

We are given that the distribution of life of television sets is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the value of x such that the probability is 0.03.

`P( X < x) = P( z < \displaystyle(x - 36)/(8))=0.03`

Calculation the value from standard normal z table, we have,

`\displaystyle(x - 36)/(8) =-1.881\\\\x = 20.952\approx 20.95`

Thus, the company should guarantee a lifetime of less than or equal to 20.95 years so that less than 3% of the television sets fail while under warranty.