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MATH 1131 3.0  Fall 2011
Assignment 2
(Due Date: Oct 19, 2011)
(hand in all questions)
Question 1:
Suppose that in a weekly lottery you have probability .02 of winning a prize
with a single ticket and that you buy 1 ticket per week for 52 weeks.
a. (2 marks) What is the probability that you win no prizes?
b. (2 marks) What is the probability that you win 3 or more prizes?
c. (2 marks) What is the mean and standard deviation of the number of prizes you win?
Solution:
Let
X
be the number of weeks that you win; then
X
is a binomial rv with
n
= 52 and
p
= 0
.
02.
(a) P(X=0) = 0.350;
(b)
P
(
X
≥
3) = 1

P
(
X
≤
2) = 1

P
(
X
= 0)

P
(
X
= 1)

P
(
X
= 2) = 0
.
0859.
(c) E(X) = 52(0.02) = 1.04; Standard deviation of
X
=
q
52(0
.
98)(0
.
02) =
√
1
.
0192 =
1
.
01.
Question 2:
An appliance dealer sells three diﬀerent models for upright freezers have
13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let
X
= the amount of storage
space purchased by the next customer to buy a freezer. Suppose that
X
has the following
probability distribution:
X
13.5 15.9 19.1
P
(
X
=
x
)
.2
.5
.3
a. (3 marks) Find the mean and standard deviation of X.
b. (3 marks) If the price of the freezer depends on the size of the storage space, X, such
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 Fall '10
 Wong
 Statistics, Probability

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