Find an Online Tutor Now

Davina D.

asked • 04/20/16

help with a problem and is there any way to check my answer so i am not double guessing?

An elevator has a stated maximum capacity of 12 people or 2004 pounds. If 12 people have weights with a mean greater than (2004/12) = 167 pounds, the capacity will be exceeded. Assume that weights of men are normally distributed with a mean of 182.9 pounds and a standard deviation of 40.8 pounds. Show your work and round your answers to FOUR decimal places.
a. Compute the probability that a randomly selected man will have a weight greater than 167 pounds.
b. Compute the probability that 12 randomly selected men will have a mean weight that is greater than 167 pounds.
c. Does the elevator appear to have the correct weight limit? Why or why not?
 
 
mean = 182.9 SD = 40.8
 
 
a. z(167)=(167-182.9)/40.8=-0.389706 or -0.3897
p(z>-0.3897)=0.3520.....using the z score table
 
b. z= (169-182.9)/[40.8/√(12)] = -1.180172 or -1.1802
 
p(z>-1.1802)=0.1190
 
c. No there is a good chance that 12 randomly selected people will exceed the elevator capacity. 
 
How could i check my work so that I know I was on the right track because I  think I did this correctly but I could be wrong.
 

2 Answers By Expert Tutors

By:

Arnold F. answered • 04/20/16

Tutor
5 (53)

College Professor & Expert Tutor In Statistics and Calculus

Davina D.

I see where my mistakes were made but i dont see where you have come up with .3133 + .5?
Report

04/20/16

Arnold F.

I looked up z=-.39 in the table to get .3133 (area between -.39 and 0) and then added .5 to get the rest of the area since we want between -.39 and infinity.
 
 
Report

04/20/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.