3 - THU



1. Thirty students in the School of Business were asked what their majors were. The following represents their responses (M = Management; A = Accounting;

E = Economics; O = Others).

|A |M |M |A |M |M |E |M |O |A |

|E |E |M |A |O |E |M |A |M |A |

|M |A |O |A |M |E |E |M |A |M |

a. Construct a frequency distribution and a bar graph.

b. Construct a relative frequency distribution and a pie chart.

Answers: (a) (b)

Relative

Major Frequency Frequency

M 12 0.4

A 9 0.3

E 6 0.2

O 3 0.1

Total 30 1.0

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2. The following data show the yearly salaries of football coaches at some state supported universities.

| | |Salary |

| |University |(in $1,000) |

| |A |53 |

| |B |44 |

| |C |68 |

| |D |47 |

| |E |62 |

| |F |59 |

| |G |53 |

| |H |94 |

For the above sample, determine the following measures.

a. The mean yearly salary

b. The standard deviation

c. The mode

d. The median

e. The 70th percentile

Answers:

a. 60

b. 15.8

c. 53

d. 56

e. 62

3. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.

Selected Major

|Gender |Management |Marketing |Others |Total |

|Male |40 |10 |30 |80 |

|Female |30 |20 |70 |120 |

|Total |70 |30 |100 |200 |

a. What is the probability of selecting an individual who is majoring in Marketing?

b. What is the probability of selecting an individual who is majoring in Management, given that the person is female?

c. Given that a person is male, what is the probability that he is majoring in Management?

d. What is the probability of selecting a male individual?

Answers:

a. 0.15

b. 0.25

c. 0.50

d. 0.40

4. In a random sample of UTC students 50% indicated they are business majors, 40% engineering majors, and 10% other majors. Of the business majors, 60% were females; whereas, 30% of engineering majors were females. Finally, 20% of the other majors were female.

a. What percentage of students in this sample was female?

b. Given that a person is female, what is the probability that she is an engineering major?

Answers:

a. 44%

b. 0.2727

5. Seventy percent of the students applying to a university are accepted. Using the binomial probability tables, what is the probability that among the next 18 applicants

a. At least 6 will be accepted?

b. Exactly 10 will be accepted?

c. Exactly 5 will be rejected?

d. Fifteen or more will be accepted?

e. Determine the expected number of acceptances

f. Compute the standard deviation.

Answers:

a. 0.9988

b. 0.0811

c. 0.2017

d. 0.1646

e. 12.6

f. 1.9442

6. Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected.

a. What is the probability that the sample contains exactly 4 minorities?

b. What is the probability that the sample contains fewer than 2 minorities?

c. What is the probability that the sample contains exactly 1 non-minority?

d. What is the expected number of minorities in the sample?

e. What is the variance of the minorities?

Answers:

a. 0.0577

b. 0.4450

c. 0.0013

d. 1.75

e. 1.3125

7. On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour.

a. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.

b. Compute the probability that exactly 5 cars will arrive in the next hour.

c. Compute the probability that no more than 5 cars will arrive in the next hour.

Answers:

a. Poisson; it shows the probability of x occurrences of the event over a time period.

b. 0.1385

c. 0.3406

8. Compute the hypergeometric probabilities for the following values of n and x. Assume N = 8 and r = 5.

a. n = 5, x = 2

b. n = 6, x = 4

c. n = 3, x = 0

d. n = 3, x = 3

Answers:

a. 0.1786

b. 0.5357

c. 0.01786

d. 0.1786

9. A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers.

a Can a binomial formula be used for the solution of the above problem?

b. What kind of probability distribution does the above satisfy, and is there a function for solving such problems?

c. What is the probability that both customers received damaged VCRs?

d. What is the probability that one of the two customers received a defective VCR?

Answers:

a. No, in a binomial experiment, trials are independent of each other.

b. Hypergeometric probability distribution

c. 0.2

d. 0.6

10. The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes.

a. What is the probability that a guitar neck can be carved between 95 and 165 minutes?

b. What is the probability that the guitar neck can be carved between 120 and 200 minutes?

c. Determine the expected completion time for carving the guitar neck.

d. Compute the standard deviation.

Answers:

a. .6875

b. .875

c. 150

d. 23.09

11. The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000.

a. What is the probability that a randomly selected employee will have a starting salary of at least $31,000?

b. What percentage of employees has salaries of less than $12,200?

c. What are the minimum and the maximum salaries of the middle 95% of the employees?

d. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation?

Answers:

a. 0.1151

b. 0.52%

c. minimum = $15,200 maximum = $34,800

d. 4,000

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