Answer:
If the average life is less than 6.24 years, then, it lies in the lower 3% and willing to be replaced.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 10
Standard Deviation, σ = 2
We assume that the distribution of average life is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(X<x) = 0.03
We have to find the value of x such that the probability is 0.03.
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 10}{2})=0.03[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<-1.881) = 0.03[/tex]
[tex]\displaystyle\frac{x - 10}{2} = -1.881\\x = 6.238[/tex]
Hence, if the average life is less than 6.24 years, then, it lies in the lower 3% and willing to be replaced.
