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 38 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 080 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 6 comma 080 l b Over 38 EndFraction equals 160 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 174.2 lb and a standard deviation of 38.4.

Answer #1

for normal distribution z score =(X-μ)/σ | |

here mean= μ= | 174.2 |

std deviation =σ= | 38.4000 |

sample size =n= | 38 |

std error=σ_{x̅}=σ/√n= |
6.2293 |

probability that the aircraft is overloaded :

probability = | P(X>160) | = | P(Z>-2.28)= | 1-P(Z<-2.28)= | 1-0.0113= |
0.9887 |

as probability of it being overloaded is highly probable ; therefore one should lower the number of passenger it accommodated,

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 40 passengers, and a flight has
fuel and baggage that allows for a total passenger load of 6 comma
520 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 6 comma...

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 42 passengers, and a flight has
fuel and baggage that allows for a total passenger load of 6,804
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
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Part One
Before every flight, the pilot must verify that the total
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7626,762 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...

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