The capacity of an elevator is 8 people or 1264 pounds. The capacity will be exc
ID: 3317988 • Letter: T
Question
The capacity of an elevator is 8 people or 1264 pounds. The capacity will be exceeded if 8 people have weights with a mean greater than 1264 / 8=158 pounds. Suppose the people have weights that are normally distributed with a mean of 160lb and a standard deviation of 35lb.
a. Find the probability that if a person is randomly selected, his weight will be greater than 158 pounds.
The probability is approximately =___
b. Find the probability that 8 randomly selected people will have a mean that is greater than 158 pounds.
The probability is approximately=___
c. Does the elevator appear to have the correct weight limit? Why or why not?
A.Yes, 8 randomly selected people will always be under the weight limit.
B.No, there is a good chance that 8 randomly selected people will exceed the elevator capacity.
C. No,8 randomly selected people will never be under the weight limit.
D.Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity
Explanation / Answer
Solution:- mean = 160 lb , sd = 35
a. P(X > 158) = P(Z > (158-160)/35)
= P(Z > -0.0571)
= 0.5239
b)P(X > 158) = P(Z > (158-160)/(35/sqrt(8))) There fore n= 8
= P(Z > -0.1616)
= 0.5636
c) option D. Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity.
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