Question

Elevator ride: Engineers are designing a large elevator that will accommodate 50 people. The maximum weight the
elevator can hold safely is 9450 pounds. According to the National Health Statistics Reports, the weights of adult
U.S. men have mean 163 pounds and standard deviation 63 pounds, and the weights of adult U.S. women have mean 159 pounds
and standard deviation 72 pounds. Use the TI-84 Plus calculator.

Part 1 of 3
(a) If 50 people are on the elevator, and their total weight is 9450 pounds, what is their average weight?
The average weight is___ pounds.

Part 2 of 3
(b) If a random sample of 50 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places.
The probability that the maximum safe weight will be exceeded is?

Part 3 of 3
(c) If a random sample of 50 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places.
The probability that the maximum safe weight will be exceeded is?

Answer 1

a) The average weight is 9450/50= 189 pounds

b)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	163
std deviation   =σ=	63.000
sample size       =n=	50
std error=σx̅=σ/√n=	8.90955

probability =P(X>189)=P(Z>(189-163)/8.91)=P(Z>2.92)=1-P(Z<2.92)=1-0.9982=0.0018

Note:

if using ti-84 use command :normalcdf(189,1000000,163,8.9095)

c)

here mean=       μ=	159
std deviation   =σ=	72.0000
sample size       =n=	50
std error=σx̅=σ/√n=	10.1823

probability =P(X>189)=P(Z>(189-159)/10.182)=P(Z>2.95)=1-P(Z<2.95)=1-0.9984=0.0016

Note: if using ti-84 use command :normalcdf(189,1000000,159,10.1823)