The weight of people in a small town in Missouri is known to be normally distrib
ID: 3364711 • Letter: T
Question
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 177 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,528 pounds or 18 persons.” What is the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds?
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 177 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,528 pounds or 18 persons.” What is the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds?
Explanation / Answer
expected value of 18 persons =18*177 =3186
and std deviation =18*(28)1/2 =95.247
therefore probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds
=P(X>3528) =1-P(X<3528)=1-P(Z<(3528-3186)/95.247) =1-P(Z<3.5907)=1-0.9998 =0.0002
please revert for any clarification required
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