Question 1090617: The capacity of a lift is 15 people or 2385 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2385/15=159 pounds. Suppose the people have weights that are normally distributed with a mean of 163 pounds and a standard deviation of 32 lb
a.Find the probability that if a person is randomly selected, his weight will be greater than 159 pounds
Find the probability that 15 randomly selected people will have a mean that is greater than 159 pounds
Does the elevator appear to have the correct weight limit? Why or why not?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The capacity of a lift is 15 people or 2385 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2385/15=159 pounds. Suppose the people have weights that are normally distributed with a mean of 163 pounds and a standard deviation of 32 lb
a.Find the probability that if a person is randomly selected, his weight will be greater than 159 pounds
z(159) = (159-163)/32 = -0.125
P(x > 159) = P(z > -0.125) = normalcdf(-0.125,100) = 0.5497
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Find the probability that 15 randomly selected people will have a mean that is greater than 159 pounds
z(159) = (159-163)/32/sqrt(15) = -0.4841
P(x-bar > 159) = P( z > -0.4841) = normalcdf(-0.4841,100) = 0.6859
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Does the elevator appear to have the correct weight limit? Why or why not?
No. More that 68% of groups of 15 will exceed the capacity of the lift.
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Cheers,
Stan H.
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