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# STATISTICS: Probability Problems

8.A sample of 2,000 licensed drivers revealed the following number of speeding violations.
Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000
What is the experiment?
List one possible event.
What is the probability that a particular driver had exactly two speeding violations?
What concept of probability does this illustrate?

66. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:
Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500
What is the probability of selecting a female student?
What is the probability of selecting a finance or accounting major?
What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
Are gender and major independent? Why?
What is the probability of selecting an accounting major, given that the person selected is a male?
Suppose two students are selected randomly to attend a lunch with the president of the university.
What is the probability that both of those selected are accounting majors?

Chapter 7
38. One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If a garage is robbed, what is the probability the doors were left open?

44. A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

60.Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the graduation.
1. What is the probability both of the selected students plan to attend college?
2. What is the probability one of the two selected students plans to attend college?

1. The mean life of a computer disk drive is 2,000 hours. The standard deviation is 140 hours. Assuming the life-time of the drives to be normally distributed, find the probability of a disk drive lasting more than 1,800 hours.
a. .4236
b. .9236
c. .8472
d. .5764
e. .2118
f. None of the above.

2. The yearly commissions per salesperson employed by a manufacturer of light machinery average \$40,000 with a standard deviation of \$5,000. What percent of the salespersons earn between \$32,000 and \$42,000?
a. 60.06%
b. 39.94%
c. 34.13%
d. 65.87%
e. 81.66%
f. None of the above.

3. A study of 200 stamping firms revealed these incomes after taxes:

Income After Taxes Number of Firms
Under \$1 million 102
\$1 million up to \$20 million 61
\$20 million and more 37

What is the probability that a particular firm selected has under \$1 million in income after taxes?
a. 0.000
b. 0.250
c. 0.333
d. 0.510
e. None of the above.

4. A study of the opinion of designers with respect to the primary color most desirable for use in executive offices showed that:

Primary Color Number of Opinions
Red 92
Orange 86
Yellow 46
Green 91
Blue 37
Indigo 46
Violet 2

What is probability that a designer does not prefer red?
a. 1.000
b. 0.770
c. 0.000
d. 0.230
e. None of the above.

#### Solution Preview

Please find the solution of the probability problems in the attached word file.

b. Lind Chapter 5: Exercises 8, 66
c. Lind Chapter 7: Exercises 38, 44, 60

Chapter 5

8.A sample of 2,000 licensed drivers revealed the following number of speeding violations.
Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000
What is the experiment?
ANSWER: In the present experiment we discuss the possibilities of the violation in the Drivers.
List one possible event.
Answer: There are total no. of drivers = 2000
Then 12 driver revealed speed 3 times
This is an event.

What is the probability that a particular driver had exactly two speeding violations?
There are 18 driver who had exactly two seeding violations out of 2000
Then probability is = 18 /2000 = 0.009
What concept of probability does this illustrate?
The concept of the probability which use in this experiment that illustrate what is
possibility speeding violence in drivers.

66. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:
Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500
What is the probability of selecting a female student?
There are total no. of student 500
And no. of female student = 200
Then probability of choosing female student = 200/500 = 0.4

What is the probability of selecting finance or accounting major?
There are total finance student = 100
There are total accounting student = 200
Then total accounting or finance student = 200 +100 = 300
Therefore probability of selecting finance or accounting major = 300/500 = 0.6
What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
There are female student = 200 , and accounting student = 200 but there are total 100 student who are ...

#### Solution Summary

Detailed solutions to problems.

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