SOLUTION: An airline knows that the mean weight of all pieces of passengers’ luggage is 49.9 lb with a standard deviation of 8.3 lb. What is the probability that the weight of 69 bags in

Question 1189757: An airline knows that the mean weight of all pieces of passengers’ luggage is 49.9 lb with a standard deviation of 8.3 lb. What is the probability that the weight of 69 bags in a cargo hold is more than the plane’s total weight capacity of 3,640 lb?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
average weight of each piece of luggage is equal to the total weight of all pieces of luggage divided by the number of pieces of luggage.
total weight of all pieces of luggage is equal to the average weight of each piece of luggage multiplied by the number of pieces of luggage.
there are 69 pieces of luggage.

the total luggage capacity of the plane is less than or equal to 3640 pounds.
this mean that the average weight of each piece of luggage must be less than or equal to 3640 / 69 = 52.75362319 pounds.

what this problem becomes is:
what is the probability that the average weight of each piece of luggage in the sample is greater than 52.75362319 pounds.

use the z-score formula to figure this out.
the z-score formula is z = (x - m) / s
z is the z-score
x is the mean weight of the sample.
m is the mean weight of all passenger's luggage.

standard deviation of all passenger's luggage is 8.3 pounds.
sample size is 69
standard error is standard deviation divided by square root of sample size = 8.3 / sqrt(69) = .9992025806.

round to 4 decimal places to get standard error = .9992.
z-score formula becomes z = (52.75362319 - 49.9) / .9992 = 2.8559 rounded to 4 decimal places.

the probability of getting a z-score greater than 2.8559 is equal to .0021 rounded to 4 decimal places.

that becomes the probability that the total weight in the cargo hold will be greater than 69 * 52.75362319 = 3640 pounds.

your solution is that the probability that the weight of the 69 pieces of luggage will be greater than 3640 pounds is equal to .0021.

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