Question

A small jet can carry up to 40 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 196 pounds, with a standard deviation of 63 pounds. What is the probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Answer 1

mean = 196 * 43 = 8428

std. dev. = 63 * sqrt(43) = 413.1186

Here, μ = 8428, σ = 413.1186 and x = 9200. We need to compute P(X >= 9200). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (9200 - 8428)/413.1186 = 1.87

Therefore,
P(X >= 9200) = P(z <= (9200 - 8428)/413.1186)
= P(z >= 1.87)
= 1 - 0.9693
= 0.031