According to the FAA the mean weight of airline passengers and crew is u = 190 pounds with a standard deviation of a = 35 pounds. Suppose that a JJ Airways Airbus plane takes off with 196 random passengers and crew (souls) on board. Let M be the random variable representing the mean weight of the 196 souls on board. Let T be the random variable representing the total weight the 196 souls on board. a) What theorem will let us treat T and M as approximately normal random variables? O Chebychev's Theorem O Central Limit Theorem O Convolution Theorem O Monte Carlo Theorem O 301 Theorem O Law of Large Numbers

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According to the FAA the mean weight of airline passengers and crew is μ = 190 pounds with a standard deviation of a = 35 pounds. Suppose that a JJ Airways Airbus plane takes off with 196
random passengers and crew (souls) on board. Let M be the random variable representing the mean weight of the 196 souls on board. Let T be the random variable representing the total weight of
the 196 souls on board.
a) What theorem will let us treat T and M as approximately normal random variables?
O Chebychev's Theorem
O Central Limit Theorem
O Convolution Theorem
O Monte Carlo Theorem
O 301 Theorem
O Law of Large Numbers
b) What is the expected value of T?
c) What is the standard deviation of T?
d) What is the approximate probability that T is greater than 38000 pounds?
e) What is the 80th percentile of the approximate distribution of T?
f) What is the expected value of M?
g) What is the standard deviation of M?
h) What is the approximate probability M is greater than 196 pounds?
Transcribed Image Text:According to the FAA the mean weight of airline passengers and crew is μ = 190 pounds with a standard deviation of a = 35 pounds. Suppose that a JJ Airways Airbus plane takes off with 196 random passengers and crew (souls) on board. Let M be the random variable representing the mean weight of the 196 souls on board. Let T be the random variable representing the total weight of the 196 souls on board. a) What theorem will let us treat T and M as approximately normal random variables? O Chebychev's Theorem O Central Limit Theorem O Convolution Theorem O Monte Carlo Theorem O 301 Theorem O Law of Large Numbers b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 38000 pounds? e) What is the 80th percentile of the approximate distribution of T? f) What is the expected value of M? g) What is the standard deviation of M? h) What is the approximate probability M is greater than 196 pounds?
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