Question

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 154 lb, that the standard deviation is 27 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:

What is the expected value of the sample mean of their weights?
μ_x =  lb

(b) What is the standard deviation of the sampling distribution of the sample mean weight? (Round your answer to two decimal places.)
σ_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.)
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

Solution :

Given that,

mean = = 154

standard deviation = = 27

a ) n = 16

= 154

b ) ₌ / n

= 27 16

= 6.75

_{= 6.75}

c ) 2500 / 16 = 156.25

d ) P ( >156.25 )

= 1 - P ( < 156.25 )

= 1 - P ( - / ) < ( 156.25 - 154 / 6.75)

= 1 - P ( z < 2.25 / 6.75 )

= 1 - P ( z < 0.33 )

Using z table

= 1 - 0.6293

= 0.3707

Probability = 0.3707