Answer to Question #128155 in Statistics and Probability for mahi

Question

Studies sows that CNG use for Sedan car sold in India is normally distributed with a
mean of 25.5km/ kg and a standard deviation of 4.5km/g. To get a competitive edge, a
manufacturer wishes to develop a Sedan car that outperforms 95% of the existing sedan
in fuel economy, what must be the CNG use rate for the new car be ?

Answer 1

Let $X$ be  the CNG use rate: $X\sim N(\mu, \sigma^2)$

Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

Given $\mu=25.5, \sigma=4.5$

$$P(X<x)=0.95$$

$$P(Z<z_c)=0.95=>z_c=1.645$$

$$x=\mu+z_c\times\sigma$$

$$x=25.5+1.645\times4.5=32.9025\approx32.9$$

The CNG use rate for the new car must be 32.9 km/ kg