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

194

pounds and standard deviation

68

pounds, and the weights of adult U.S. women have mean

164

pounds and standard deviation

77

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

60

adult women ride the coaster, the probability that the maximum safe weight will be exceeded is

Answer 1

a)

The average weight is =12000/60=200

b)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	194
std deviation   =σ=	68.000
sample size       =n=	60
std error=σx̅=σ/√n=	8.77876

probability =P(X>200)=P(Z>(200-194)/8.779)=P(Z>0.68)=1-P(Z<0.68)=1-0.7528=0.2472

C)

probability =P(X>200)=P(Z>(200-164)/9.941)=P(Z>3.62)=1-P(Z<3.62)=1-0.9999=0.0001