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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 Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 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 6200lb/37 = 167.6lb. 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 185.47 lb and a standard deviation of 39 lb. make sure to include pdf
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 Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 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 6200lb/37 = 167.6lb. 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 185.47 lb and a standard deviation of 39 lb. make sure to include pdf
Using thenormal probability distribution and the central limit theorem, it is found that theprobabilityis of0.9974 = 99.74%,which means that the pilotshould take action.Normal Probability DistributionIn a normal distribution withmeanandstandard deviation, thez-scoreof ameasure Xis given by:Itmeasureshow many standard deviations the measure is from the mean.After finding the z-score, we look at the z-score table and find thep-valueassociated with this z-score, which is thepercentileof X.By theCentral Limit Theorem, the sampling distribution of sample means of size n has standard deviation.In this problem, for the population, themeanand thestandard deviationare given by, respectively:.For asample of 37passengers, we have that:Theprobabilitythat the aircraft is overloaded isone subtracted by the p-value of Z when X = 167.6, hence:By the Central Limit Theorem:has a p-value of 0.0026.1 - 0.0026 = 0.9974.There is a0.9974 = 99.74% probabilitythat the aircraft is overloaded. Since this is a very high probability, the pilotshould take action.To lern more about thenormal probability distribution and the central limit theorem, you can checkbrainly.com/question/24663213...