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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.03.
[tex]P( X < x) = P( z < \displaystyle\frac{x - 36}{8})=0.03[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 36}{8} =-1.881\\\\x = 20.952\approx 20.95[/tex]
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.
