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

Answer:

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.    

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

$P( X < x) = P( z < \displaystyle\frac{x - 36}{8})=0.03$  

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

$\displaystyle\frac{x - 36}{8} =-1.881\\\\x = 20.952\approx 20.95$  

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.