Question

The mean operating cost of a 737 airplane is $2,071 per day. Suppose you take a sample of 49 of these 737 airplanes and find a mean operating cost of $2,050 with a sample standard deviation of $106.

a. What is the probability that a 737 will have an operating cost that is greater than the sample mean you have found?

b. What is the probability that a plane would have an operating cost that is between $2,050 and $2,088.60 per day?

Answer 1

a)

Here, μ = 2050, σ = 15.1429 and x = 2071. We need to compute P(X >= 2071). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (2071 - 2050)/15.1429 = 1.39

Therefore,
P(X >= 2071) = P(z <= (2071 - 2050)/15.1429)
= P(z >= 1.39)
= 1 - 0.9177 = 0.0823

b)

Here, μ = 2050, σ = 15.1429, x1 = 2050 and x2 = 2088.6. We need to compute P(2050<= X <= 2088.6). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (2050 - 2050)/15.1429 = 0
z2 = (2088.6 - 2050)/15.1429 = 2.55

Therefore, we get
P(2050 <= X <= 2088.6) = P((2088.6 - 2050)/15.1429) <= z <= (2088.6 - 2050)/15.1429)
= P(0 <= z <= 2.55) = P(z <= 2.55) - P(z <= 0)
= 0.9946 - 0.5
= 0.4946