The capacity of an elevator is 10 people or 1630 pounds. The capacity will be ex
ID: 3380072 • Letter: T
Question
The capacity of an elevator is 10 people or 1630 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1630/10=163 pounds.
Suppose the people have weights that are normally distributed with a mean of 168 lb and a standard deviation of 26 lb.
(a) Find the probability that if a person is randomly selected, his weight will be greater than 163 pounds. (Round to four decimal places as needed.)
(b) Find the probability that 8 randomly selected people will have a mean that is greater than 163 pounds.
(c) Does the elevator appear to have the correct weight limit? Why or why not?
Explanation / Answer
Capcity of elevator = 1630 pounds
Weight of any person is normal (168, 26)
a) P(X>163) = P(Z>-5/26)
= P(Z>-0.19) = 0.5753
b) When n =8
std error = 26/rt8 = 9.192
P(X>163) = P(Z>-5/9.192)
= P(Z>-0.54)
= 0.7088
c) For checking this let us consider sample of 10 persons
n =10
Std error = 26/rt10
= 8.2
P(X>163)
= P(z>-5/8.2)
= P(z>-0.61)
= 0.7291
No, the elevator does not appear to have correct weight limit
As prob for any random sample exceeding the prescribed weight = 0.7291 very high.
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