Question

According to the Air transport Association of America, the average operating cost of an MD-80 Jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 Jet airliner are normally distributed with a standard deviation of $162 per hour.

a) At what operating cost would only 20% of the operating cost be less?

b)At what operating cost would 65% of the operating costs be more?

c) What operating cost would be more than 85% of operating costs

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = $2,087 per hour

Standard deviation = $162 per hour

a) Let the 20% of the operating cost be less that T

P(X < T) = 0.2

P(Z < (T - 2087)/162) = 0.2

Take Z score corresponding to 0.2 from standard normal distribution table

(T - 2087)/162 = -0.84

T = $1950.92 per hour

b) Let the 65% of the operating cost be more that S

P(X > S) = 0.65

P(X < S) = 1 - 0.65 = 0.35

P(Z < (S - 2087)/162) = 0.35

Take Z score corresponding to 0.35 from standard normal distribution table

(S - 2087)/162 = -0.385

S = $2024.63 per hour

c) Let the 85% of the operating cost be less that E

P(X < E) = 0.85

P(Z < (E - 2087)/162) = 0.85

Take Z score corresponding to 0.85 from standard normal distribution table

(E - 2087)/162 = 1.04

E = $2255.48 per hour