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## Sample Document Text

STAT 4705 Test II March 26, 2004 N
1; 1 . . An elevator is being designed to accommodate 10 people, and the nominal maximum
/ capacity is to be set at 1800 lb. It is estimated that the distribution of the weight of
people who will be riding on this elevator can be modeled as a normal distribution
with mean Jl = 160 lb and standard deviation (J" = 40 lb. If 10 people ride on this
elevator then the total weight of these 10 people can be represented as T = L}~l Xi ,
where Xi is the weight of the ith person.
(a) If 10 people ride on the elevator, and the weights of these 10 people are
independent, find the probability that the total weight T will exceed the nominal
capacity of 1800 lb.
vtA -;: I 6 "(ib
.1"
Y :- Ljb"Q
riz ::-,)")
1- f(z '-.~)
- I - ,G q I~-
-I~ I
(b) Suppose that it is desirable to design the elevator with a nominal capacity, say c,
such that the probability of the total weight of 10 people exceeding c is only .005.
Find c.
l-p(~ '- :-L) =,.OO~'
X - Jb,o-O ...

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