Question

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 35 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 5 comma 880 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than StartFraction 5 comma 880 l b Over 35 EndFraction equals 168 lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 174.9 lb and a standard deviation of 35.2.

Answer 1

0.8770

Explanation:

We are dealing with a mean of a sample, so we use the formula

`z=\frac{\bar{X}-\mu}{\sigma / √(n)}`

Our mean, μ, is 174.9 and our standard deviation, σ, is 35.2. Our sample size, n, is 35. To find P(X > 168),

z = (168-174.9)/(35.2÷√35) = -6.9/(35.2÷5.9161) = -6.9/5.9499 = -1.16

Using a z table, we see that the area under the curve to the left of this value is 0.1230. However, we want the area to the right; this means we subtract from 1:

1-0.1230 = 0.8770