Practice/Assessment Masters Answers
CHAPTER 7 Probability Distributions
7.1 Probability Distributions
1.
2.
3.
0; Answers will vary.
Answers will vary.
a) 10 400 000
1
1
1
b) P(x):
,
,
,
10 400 000 2 080 000 416 000
1
1
1
,
,
10 4 000 10 400 2080
3.
c) $1.27
d) $3.73
b) P(x):
0
5
,
37 575 681 37 575 681
376
21 957
467 174
,
,
,
37 575 681 37 575 681 37 575 681
425 961
4.
5.
,
37 575 681
a) P(x): 0.125, 0.375, 0.375, 0.125
b) E(x)=1.5
4-sided die
4.. 4.68 baskets
5.
6.
7.
7.2 Binomial Distributions
2.
A binomial distribution has a specified number
of independent trials in which the outcome is
either success or failure. The probability of a
success is the same in each trial.
x
0
1
2
3
4
5
6
7
8
9
10
P(x)
0.0060
0.0403
0.1209
0.2150
0.2508
0.2007
0.1115
0.0425
0.0106
0.0016
0.0001
13.5%
0.000 122 5
a) 0.2503
b) 0.4744
c) 2.5
7.3 Geometric Distributions
1.
1.
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
P(x): 0.0282, 0.1211, 0.2335, 0.2668, 0.2001,
0.1029, 0.0368, 0.0090, 0.0014,
1.3778  104, 5.9049  106
2.
3.
4.
5.
The trials are independent and have two
possible outcomes, with the probability of
these outcomes being constant in each trial.
We are concerned with the waiting time
until a 3 is rolled, so a geometric
distribution is necessary.
a) 0.026 84
b) 4 shots
a) 0.001 98
b) 0.011 94
c) 499 motors
a) 0.016 01
b) 49 trials
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
P(x): 0.3333, 0.2222, 0.1481, 0.098 77,
0.065 84, 0.043 90, 0.029 26, 0.019
51, 0.013 01, 0.008 671
7.4 Hypergeometric Distributions
Copyright © 2003 McGraw-Hill Ryerson Limited
Chapter 7 Answers  MHR 87
1.
2.
3.
4.
5.
The random variable in a hypergeometric
distribution is the number of successful
outcomes in the specified number of trials.
a) x: 0, 1, 2,3, 4, 5, 6
P(x): 0.000 053 87, 0.003 878,
0.053 33, 0.237 02, 0.399 97, 0.255 98,
0.049 77
b) 4 women
3 women
x: 0, 1, 2, 3, 4, 5
P(x): 0.001 68, 0.025 21, 0.135 75, 0.329 67,
0.362 64, 0.145 05
1200
Study Master, Chapter 7
1.
2.
3.
a) hypergeometric
b) geometric
c) hypergeometric
d) binomial
e) uniform
f) binomial
g) hypergeometric
h) geometric
$0.35
a) Answers may vary. For example,
P(2)
P(1)
P(3)
P(5)
P(4)
b) Lose 1.5
c)
P(x)
0.5
0.4

0.3
0.2



1
6.
x: 0, 1, 2
P(x): 0.1667, 0.1389, 0.1157
8. 1.2 free throws
9. a) 0.9325
b) 1.4 days
10. a) 1.4286
11. 43
Alternate Test, Chapter 7
1.
a) geometric
b) hypergeometric
c) uniform
d) binomial
2. $0.14
3. a) 0.3359
b) 0.2066
c) 0.9
d) 1.8
4. 120.95 cm2
5. a) x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
P(x): 0.107 374 182 400,
0.268 435 456 000,
0.301 989 888.000,
0.201 326 592 000,
0.088 080 384 000,
0.026 424 115 200,
0.005 505 024 000,
0.000 786 432 000,
0.000 073 728 000,
0.000 004 096 000,
0.000 000 102 400
b) 200
6. a) 0.5981
b) 5 rolls
7. Answers may vary.
8. a) 0.7373
b) 0.05792
c) 1
9. 0.093 75
10. Answers may vary.
11. 750 raccoons

0.1
4.
5.
7.
2
3
4
Region (x)
5
d) E(x) is not zero.
e) Answers will vary.
0.9996
a) x: 0, 1, 2, 3, 4
P(x): 0.1296, 0.3456, 0.3456, 0.1536, 0.0256
b) 1.6
a) 0.0544
b) 3
88 MHR  Chapter 7 Answers
Copyright © 2003 McGraw-Hill Ryerson Limited