Question

Problem #1 (10 points)
Suppose you must establish regulations concerning the maximum number of people who can occupy an
elevator. A study of elevator occupancies indicates that, if eight people occupy the elevator, the probability
distribution of the total weight of the eight people has a mean equal to 1,200 pounds and a variance equal
to 9,800 lbs2
. Assume that the probability distribution is approximately normal. We are interested in the
probabilities of exceeding 1,300 pounds and 1,500 pounds in the elevator.
Requirements:
1. Draw for each case two normal curves (a total of 4 curves):
a) A normal curve showing the values for the mean and the value of X.
b) A normal curve showing the normalize values for the mean and the value of X
2. The probability that the total weight of eight people exceeds 1,300 pounds is:
a. 0.1143
b. 0.1562
c. 0.1645
d. 0.5540
The Probability that the total weight of eight people exceeds 1,500 pounds is:
a. 0.0012
b. 0.2012
c. 0.4012
d. 0.6012

Answer 1

Let Xbe totsl weight of eight people XN1200, 9800 G-」9800 こ98:995 200 200 1300 PXISo N(1200, 93.95 1200 1520

Li 48-99S Lising 2table, Ansuoer is x15DOPX 1500-1200 1.01 98.995 3.03 Ans uer@ L._