Answer to Question #128155 in Statistics and Probability for mahi

Question #128155
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 ?
1
Expert's answer
2020-08-03T18:35:39-0400

Let XX be  the CNG use rate: XN(μ,σ2)X\sim N(\mu, \sigma^2)

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

Given μ=25.5,σ=4.5\mu=25.5, \sigma=4.5


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

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

x=μ+zc×σx=\mu+z_c\times\sigma

x=25.5+1.645×4.5=32.902532.9x=25.5+1.645\times4.5=32.9025\approx32.9

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



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