A sign in the elevator of a college library indicates a limi

A sign in the elevator of a college library indicates a limit of 16 persons. In addition, there is a weight limit of 2,500 pounds. Assume that the average weight of students, faculty, and staff at this college is 150 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal.

a. What is the probability that a randomly selected student weighs more than 156 pounds?Give the appropriate probability statement, show work, and give probability to 4 decimal places.

A random sample of 16 persons from the campus will be selected.

b. What is the mean of the sampling distribution of x bar (x with the line on top, would not let me put the symbol in)?

c. What is the standard deviation of the sampling distribution of x bar?

d. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds (i.e., above what average weight)? Justify your answer.

e. What is the probability that a random sample of 16 people will have a sample mean that will exceed the weight found in part (d)? Give the appropriate probability statement, show work, and give probability to 4 decimal places.

Solution

(a)P(X>156) = P((X-mean)/s >(156-150)/27)

=P(Z>0.22) =0.4129 (from standard normal table)

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(b)mean= 150

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(c)standard deviation =s/vn =27/sqrt(16)

=6.75

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(d)mean=2500/16 =156.25

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(e) P(xbar> 156.25) = P(Z>(156.25-150)/(27/sqrt(16)))

=P(Z>0.93) =0.1762 (from standard normal table)