Download Practice problems 6 answers

Statistics and the TI-84
Practice problems 6 answers
Counting techniques and the Hyper-geometric distribution.
Exercise 1. In a signal device, there are four lights. When on, a light could be red or
green. For a signal, at least one light must be on. How many signals are possible?
3  3  3  3  1  81  1  80
answer: MULTIPLICATION PRINCIPLE:
Exercise 2. Mr. and Mrs. Fernández belong a club of 12 members. How many
committees of 5 members are possible?
answer: COMBINATIONS; 12

MODE FLOAT

12
MATH
12!
C 5 = 5!7!
 792
ENTER 2ndQUIT
PRB
3
n
Cr 5
ENTER
answer: 792
Exercise 3. (problem 2, continuation). How many committees of 5 are possible, if Mr.
Fernández must be one of the 5 members?
answer: COMBINATIONS; 11

11
MATH
PRB
3
n
11!
 330
C 4= 4!7!
Cr 4
ENTER
answer: 330
Exercise 4. (problem 2, continuation). How many committees of 5 are possible, if Mr.
Fernández must be one of the 5 members, but Mrs. Fernández must be excluded from the
committee (they argue too much)?
answer: COMBINATIONS; 10

12
MATH
PRB
3
n
10!
 210
C 4 = 4!6!
Cr 5
ENTER
answer: 792
Exercise 5. (problem 2, continuation). How many ways a selecting 5 officials are there?
answer: PERMUTATIONS;

12
MATH
PRB
2
12
 95040
P5 = 12!
7!
n
Cr 5
ENTER
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answer: 95040
Exercise 6. A buyer must decide whether or not to accept a shipment of 40 parts. The
decision is based on inspecting a random sample of 5 parts. The shipment will be
accepted If no defective parts are found. Suppose that 4 of the parts are defective.
What is the probability that the shipment will be accepted.
4
answer:

4

MATH
C0 36 C5
40 C5
MATH
PRB
PRB
C r 0  36 MATH
3
n
n
Cr 5
3
ENTER
PRB
3
n
C r 5  40
answer: .5729292045
Exercise 7. A math team of three students to assess the school math standing is randomly
formed from a group of 2 sophomores, 12 juniors and 20 seniors.
a) Find the probability that the team is composed only of seniors.
20
C3 14 C0
34 C3

20
MATH


34 MATH
PRB
3
n
PRB
3
C r 3  14 MATH
n
PRB
3
n
Cr 0
C r 3 ENTER answer:.1905080214
b) Find the probability that both sophomores are on the team.
2
answer:
C 2 32 C1
34 C 3

2

 ENTER
MATH
PRB
3
n
34 MATH
C r 2  32 MATH
PRB
3
n
PRB
3
Cr 1
n
C r 3 ENTER
answer: 0.0053475936
c) Find the probability that all three classes are represented in the team.
answer:
2
C1 12 C1  20 C1
34 C 3

2

 20 MATH
MATH
PRB
3
n
PRB 3
C r 1  12 MATH
PRB
3
C r 1  34 MATH
PRB
3
n
n
n
Cr 1
C r 3 ENTER answer:
0.080213937
Exercise 8. A lot of 20 radios has 3 defective radios. If 5 radios are selected at random
from the lot, for inspection, what is the probability that the sample has
a) no defective radios
3


3 MATH
ENTER
C 0  17 C 5 1  6188 91


 .399
15504
228
20 C 5
 PRB 3 0  17 MATH PRB 3 5  20 MATH PRB 3 5
answer: 0.399122807
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b) all 3 defective radios
3


3 MATH
ENTER
 PRB 3 3  17 MATH PRB 3 2  20 MATH PRB 3 5
answer: 0.0087719298
c) one defective radio
c) _________
3


3 MATH
ENTER
C 3  17 C2 1  136
1


 .0087719298
15504 114
20 C 5
C1  17 C 4 3  2380 35


 .4605263158
C
15504
76
20 5
 PRB 3 1  17 MATH PRB 3 4  20 MATH PRB 3 5
answer: 0.4605263158
9. From a group of 7 democrats and 12 republicans, a committee of 4 people is selected at random, what is
the probability that the committee consists of
a) all democrats?
a) _________
7


C4  12 C 0 35  1
35


 .0090299278
C
3876
3876
19 4
7 MATH
ENTER
 PRB 3 4  12 MATH PRB 3 0  19 MATH PRB 3 4
answer: 0.0090299278
b) all republicans?
answer:


7 MATH
ENTER
7
C0  12 C 4 1  495 165


 .127709783
3876
1292
19 C 4
 PRB 3 0  12 MATH PRB 3 4  19 MATH PRB 3 4
answer: 0.127709783
c) 2 democrats and 2 republicans?
7


C2  12 C2 21  66 231


 .3575851393
C
3876
646
19 4
7 MATH PRB 3 2  12 MATH PRB 3 2  19 MATH PRB 3 4
ENTER
answer: 0.3575851393
d) What is the expected number of democrats in the sample?

na
4  7 28


 1.4736
a  b 7  12 19
e) What is the standard deviation of the distribution of republicans in the sample?
2 
nab
a  b  n 4(7)(12) 7  12  4 336 15





 .7756
a  b 2 a  b  1 (7  12) 2 7  12  1 361 18
  .7756  .88
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