Question

Roller coaster ride: A roller coaster is being designed that will accommodate 60 riders. The maximum weight the
coaster can hold safely is 12,000 pounds. According to the National Health Statistics Reports, the weights of adult U.S.
men have mean 191 pounds and standard deviation 65 pounds, and the weights of adult U.S. women have mean 167 pounds and
standard deviation 74 pounds. Use the TI-84 Plus calculator.

Part 1 of 3

(a) If 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?
The average weight is____ pounds.

Part 2 of 3
(b) If a random sample of 60 adult men ride the coaster, what is the probability that the maximum safe weight
will be exceeded? Round the answer to at least four decimal places.
If a random sample 60 adult men ride the coaster, the probability that the maximum safe weight will be exceeded is?

Part 3 of 3
(c) If a random sample of 60 adult women ride the coaster, what is the probability that the maximum safe weight will
be exceeded? Round the answer to at least four decimal places.
If a random sample 60adult women ride the coaster, the probability that the maximum safe weight will be exceeded is?

Answer 1

a) average weight = 12000/60 = 200 pounds

b)

µ =    191                                      
σ =    65                                      
n=   60                                      
                                          
X =   200                                      
                                          
Z =   (X - µ )/(σ/√n) = (   200   -   191.00   ) / (   65.000   / √   60   ) =   1.073  
                                          
P(X > 200   ) = P(Z > 1.073   ) =   0.1417                     (answer)

c)

µ =    167                                      
σ =    74                                      
n=   60                                      
                                          
X =   200                                      
                                          
Z =   (X - µ )/(σ/√n) = (   200   -   167   ) / (    74   / √   60   ) =   3.454  
                                          
P(X ≥   200   ) = P(Z ≥   3.45   ) =   P ( Z <   -3.454   ) =    0.0003           (answer)