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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
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