Question

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. In addition, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. Suppose a random sample of 16 persons from the campus will be selected.

(a) What is the expected value of the sample mean of their weights? (The x in ?x has some horizontal line over it)
?x = ________ lb

(b) What is the standard deviation of the sampling distribution of the sample mean weight? (Round your answer to two decimal places.) (The x in ?x has some horizontal line over it)
?x = ________ lb

(c) What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb? (Round your answer to two decimal places.) (The follwing x has some horizontal line over it)
x > _________lb

(d) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (Round your answer to four decimal places.)
P = _________

Answer 1

Answer:a)

the expected value of the sample mean of their weight is 150

b)the standard deviation of the sampling distribution of the sample mean weight is:

Sample standard deviation = population standard deviation/ √sample size

=27/√16=6.75

c) average weights for a sample of 16 people = 2500/16 = 156.25 pounds

d)the chance that a random sample of 16 persons on the elevator will exceed the weight limit is:

P(x bar greater than 156.25) =[ z greater than (156.25-150)/6.75]

P( Z greater than 0.9259)

=0.17725