A sign in the elevator of a college library indicates a limit of 16 persons. In

Question

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. is a. hat is the probability that a randomly selected student weighs more than 156 potunds? Give the probability statements, sketch a rough picture with area of interest shaded, calculate z-score clearly showing steps and round your answer to 4 decimal places

Explanation / Answer

15.

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean ( u ) = 150
standard Deviation ( sd )= 27
sample size (n) = 16
a.
P(X > 156) = (156-150)/27/ Sqrt ( 16 )
= 6/6.75= 0.8889
= P ( Z >0.8889) From Standard Normal Table
= 0.1870
b.
mean ( u ) = 150
standard Deviation ( sd )= 27
sample size (n) = 16
c.
Yes, Normal distribution
d.
P(X > 156.25) = (156.25-150)/27/ Sqrt ( 16 )
= 6.25/6.75= 0.9259
= P ( Z >0.9259) From Standard Normal Table
= 0.1772

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