Question

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,793 per hour and a standard deviation of $439. What is the operating cost for the lowest 2% of the airplanes?

Answer 1

Answer:

x1 = 4891.294

Explanation:

given data

mean μ =  $5,793

standard deviation  σ =  $439

solution

we know here that

P(x < x1 ) = 0.02     .................1

so

$P(\frac{x-\mu }{\sigma } < \frac{x1-\mu }{\sigma }) = 0.02$

so

$P(z < \frac{x1-\mu }{\sigma }) = 0.02$

$\frac{x1-\mu }{\sigma }$  = invNorm(0.02)

so

x1 = μ + σ × invNorm(0.02)    .....................2

we use here table for invNorm(0.02) and put value in eq 2

x1 = 5793 + 439 × (-2.054 )

x1 = 4891.294