Answer to Question #216528 in Statistics and Probability for aasa

Question

Assume that the mean hourly cost to operate a commercial airplane

follows the normal 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?

Answer 1

Let $X=$ the operating cost: $X\sim N(\mu, \sigma^2).$

Given $\mu=2100, \sigma=250.$

$$P(X<\dfrac{x-2100}{250})=0.03$$

$$\dfrac{x-2100}{250}=-1.8808$$

$$x=250(-1.8808)+2100$$

$$x=\$1630$$

The operating cost for the lowest 3 percent of the airplanes is $1630.