Based on FAA estimates the average age of the fleets of the

Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a standard deviation of 1.7 years. Suppose that 40 airplanes were randomly selected from the fleets of these 10 carriers and were inspected for cracks in these airplanes that are considered too large for flying. What is the probability that the average age of these 40 airplanes is at least 14 years old?

Solution

Since n > 30, we assume a normal distribution.

So, use the z formula:
z = (xbar - ?) / ?

Where:
xbar = observed value (14)
? = mean (13.4)
? = standard deviation (1.7)

z = (xbar - ?) / ?
z = (14 - 13.4) / 1.7
z = .352941176 or .35 (rounded to 2 decimal places)