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

Question

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.

 

Answer 1

Hi Lindsay.

 

A couple of comments.

a) You've correctly calculated the Z and looked it up.  I would have selected 0.3483 rather than .0.3850 since -0.3897 is so close to -0.39 rather than -0.38.  But this is hardly significant.  What is more important is the value you looked up is the probability that z<-0.3897, not greater than.  To get the probability that the weight is > 167 #, we need to subtract the answer from the table from 1.00

So, using your value,

1.0000-0.3520 = .6480 or 64.8%

Using my value

1.0000 - 0.3483 = .6517 or 65.17%

 

b) Again you've set this up correctly and adjusted the standard deviation for the number of participants selected, but remember the z table gives us the probability of being less than not greater than.  So, subtract your answer from 1.000

1.000 - 0.119 = .881 or 88.1%

 

c)  I agree with your response to c.  With a probability that 12 men selected at random having an 88% probability that the mean of their weights is greater than 167, the capacity should be restated.  

Answer 2

I don't think you have calculated the probability correctly in a or b. Also in b you used 169 instead of 167.

 

See the table:

https://www.wyzant.com/resources/files/392716/normal_dist_table/download?encryptedID=uMpgXg5183c%3D&d=v

 

(a) .3133 + .5

 

(b) .4115 + .5