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The weight of people in a small town is known have a distribution that is unimodal and symmetric and averages 180 pounds with a standard deviation of 28 pounds. Let X represent a random variable describing the people's weight: X = weight of person; E(X) = 180 lbs; SD(X) = 28 lbs. A raft with 16 seats transports residence daily across a river. Let T represent a random variable describing the total weight of 16 people: T = total weight of 16 people.
1. Find E(T)
2. Find SD(T)
The raft has a maximum capacity of 3,200 pounds. Assuming that 16 is a large enough sample for the Central Limit Theorem to work:
3. What's the probability that a random sample of 16 passengers will exceed the weight limit? P(T ≥ 3,200 lbs).
n=16
E(x)=180
SD(x)=28

Sagot :

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