MATH 2300 026
Homework #6
Name___________________________________
Due on 3
rd
November
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the question.
1.
When a coin tossed three times, eight equally likely outcomes are possible as shown below. Let X denote the total
number of heads obtained in the three tosses. Find the probability distribution of the random variable X. Leave your
probabilities in fraction form.
A) x P(X
=
x)
0 1/16
1
1/4
2
3/8
3
1/4
B) x P(X
=
x)
1
1/4
2
7/16
3
1/4
C) x P(X
=
x)
0 1/8
1 3/8
2 3/8
3 1/8
D) x P(X
=
x)
0 1/16
1 3/16
2 3/16
3 1/16
E) x P(X
=
x)
0 0
1 1/4
2 3/8
3 1/4
2.
Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value of
where G
represents the number on the green die and R represents the number on the red die. What are the possible values of the
random variable Y?
A.

5,

4,

3,

2,

1, 0, 1, 2, 3, 4, 5
B.

6,

5,

4,

3,

2,

1, 0, 1, 2, 3, 4, 5, 6
C.
0, 1, 2, 3, 4, 5, 6
D.
0, 1, 2, 3, 4, 5
3.
The random variable X is the number of siblings of a student selected at random from a particular secondary school. Its
probability distribution is given in the table.
Find the mean of the given probability distribution.
mean
= g
G
±
²
±
³´
µ¶
·
=
G
±
¸
= ¹
0
×
7
24
º
+ ¹
1
×
13
48
º
+ ¹
2
×
3
16
º
+ ¹
3
×
7
48
º
+ ¹
4
×
1
16
º
+ ¹
5
×
1
24
º
= 1
.542
A.
1.438
B.
1.833
C.
2.5
D.
1.542
4.
The area that lies between

1.10 and

0.36
A.
0.4951
B.
0.2237
C.
0.2259
D.
0.2239
E.
0.7763
5.
Find the z

score for which the area under the standard normal curve to its left is 0.96
A.

1.38
B.
1.75
C.
1.82
D.
1.03
E.

1.75
Use the empirical rule to solve the problem.
6.
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard
deviation of 5 hours. What percentage of the bulbs has lifetimes that lie within 1 standard deviation of the mean?
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 Fall '11
 ABEYSUNDARA
 Statistics, Normal Distribution, Standard Deviation, 1.62%

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