Question

The average number of miles flown by a Boeing 777 which is operated by a commercial airline over its lifetime is 52,500,000 miles. Assume these mileage amounts have a normal probability distribution with a standard deviation of 2,975,000 miles, and find the mileage that eighty percent of the 777 fleet exceeds over the course of its lifetime in commercial aviation.

Answer 1

Solution:

Given:

$\begin{gathered} \mu=52,500,000 \\ \sigma=2,975,000 \end{gathered}$

From Z-score table, the Z-score of 80% is 0.842

Hence, using the Z-score formula,

$\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ 0.842=\frac{x-52,500,000}{2,975,000} \\ Cross\text{ multiplying;} \\ x-52,500,000=0.842\times2,975,000 \\ x-52,500,000=2,504,950 \\ x=2,504,950+52,500,000 \\ x=55,004,950miles \end{gathered}$

Therefore, the mileage that eighty percent of the 777 fleet exceeds over the course of its lifetime in commercial aviation is 55,004,950 miles