Assume that the mean hourly cost to operate a commercial air

Assume that the mean hourly cost to operate a commercial airplane follows the distribution with a mean of $2,100 per hour and a standard deviation of $ 250 What is the operating cost for the lowest 3 percent of the airplanes?

Solution

Assuming normal distribution with mean 2100 and variance (250)^2=62500

X=hourly cost of operating a airplne ~ N(2100,62500)

Y=(X-2100)/250 ~ N(0,1)

Take a such that Prob(Y<a)=0.03. Then a=Z(0.03), where Z(p) gives the pth quantile of the standard normal distribution.

So, a=-1.880794

Prob(Y<a)=Prob(X<250*a+2100)=0.03

250*a+2100=1629.802

Hence, the operating cost of lowest 3% airplanes is less than $1629.802 .