DESC 210, Spring 2004,  (PROF.  Sid Das)

HOMEWORK - 1  (35 points)

Please answer on a SCANTRON sheet.     

WRITE YOUR NAME AND CLASS TIME ON THE TOP OF YOUR SCANTRON SHEET.

Problem A

The table below shows a frequency distribution:

NUMBER OF HOURS                       FREQUENCY

            0 - 9                                                     40

            10 - 19                                                 50

            20 - 29                                                 70

            30 - 39                                                 40

BASED ON THIS TABLE - ANSWER QUESTIONS 1  THROUGH  4  BELOW.

1.   The class width for this distribution is:

a.  9                             b.  10                           c.  11                           d. 30

2.   The number of students working 19 hours or less is:

a.  40                           b.  50                           c.  90                           d. 110

3.   The Relative Frequency of students working 9 hours or less is:

a.  0.2                          b.  0.45                        c.  40                           d. 1.0

4.   The Cumulative Relative Frequency for the class 10 - 19 is:

Problem B

The sample data below has been collected for a research experiment.

5,         6,         12,       7,         6,         5,         8,         12,       5,         4

BASED ON THIS DATA - ANSWER QUESTIONS 5 THROUGH  9  BELOW.

5.   The Median is:

a.  5                             b.  6                             c.  7                             d. 8

6.   The Mode is:

a.  5                             b.  6                             c.  7                             d. 8

7.   The Mean is

a.  5                             b.  6                             c.  7                             d. 8

8.   The Third Quartile  is:

a.  5                             b.  6                             c.  7                             d. 8

9.   The Range is:

Problem C:

A bell-shaped distribution has a mean of 15 and a standard distribution of 3.1.

BASED ON THIS DATA - ANSWER QUESTIONS 10 and 11  BELOW.

10.   What percentage of data values fall between 11.9 and 18.1?

a.  95%                        b.  68%                        c.  75%                        d. Almost 100%

11.   Between what two data numbers will 95% of the data lie?

12. The mean daily sales for a company last year was $52.37 million with a standard deviation of $2 million. What percentage of sales were between $49.37 to $55.37 million.

a.  At least  55.55%      b.  At least  44.44%     c.  At least 75%            d. At least 90%

Problem D:

The table below shows the probability distribution for the daily demand of microcomputers at a local store.

DEMAND                   PROBABILITY

            0                      0.1

            1                      0.2

            2                      0.3

            3                      0.2

            4                      0.2

BASED ON THIS TABLE - ANSWER QUESTIONS 13 AND 14 BELOW.

13.  The expected daily demand is:

a.         1.0                   b.         2.2                   c.         2                      d.         4

14.  The probability of having a demand of at least two microcomputers is:

15. Consider the following population of 5 numbers: 4, 8, 10, 12, 16. The mean and the standard deviation of this population are __________ and ___________ respectively.

            A)   10 and 4.47

            B)   10 and 80

            C)   12.5 and 16

            D)   12.5 and 4

            E)   10 and 4

16. Consider the following random sample of 5 numbers: 4, 8, 10, 12, 16. The mean and the standard deviation of this sample are __________ and ____________ respectively.

            A)   10 and 4.47

            B)   10 and 80

            C)   12.5 and 16

            D)   12.5 and 4

            E)   10 and 4

17. What is the sample coefficient of variation for the following data?

            4, 8, 10, 12, 16, 10.

            A)   50%

            B)   40%

            C)   80%

            D)   160%

            E)   100%

18. If the median of a data set is 760 and the upper quartile is 950, and the lower quartile is 650, what is the interquartile range?

            A)   190

            B)   110

            C)   300

            D)   1600

            E)   1,410

19. Which of the following is a valid probability value for a discrete random variable?

            A)   .2

            B)   1.01

            C)   -.7

            D)   All of the above

20. A professor teaches two sections (sections A and B) of an introductory business statistics class. Both sections have a mean score of 75.  Section A only has 5 students and they have all received a score of 75, while section B has 15 students with a mean score of 75 and a variance of 12.  What is the standard deviation of the combined class (N = 20, treat as the population).

            A)   9                B)  6                C)  4                D)  3                E)  2

21. The average size of insurance claims processed by Good-Wish Insurance Company for the month of August is $615 with a standard deviation of $135. If you assume that the population of insurance claims is not symmetric, what is the probability that the claim is between $345 and $885?

            A)   95%          B)        88.89%            C) 55.56%       D)  84%                       E) 75%

PROBLEM E: Use the following to answer questions 22-24:

The College of Business Administration at Acorn University offers a major in Finance. Based on historical records, 30% of the College of Business students major in Finance. A random sample of 20 students is selected.

22. What is the probability that no more than 3 of the selected students are majoring in Finance?

            A)   .0716

            B)   .027

            C)   .09

            D)   .107

            E)   .0354

23. What is the probability that at least 16 of the students are not majoring in Finance?

            A)   .1304

            B)   .0716

            C)   .2374

            D)   .7626

            E)   .8696

24. What are the mean and the standard deviation of this distribution?

            A)   .3 and 2.44                                                        

            B)   3 and 4.2

            C)   6 and 4.2

            D)   6 and 2.05

25. If z is a standard normal random variable, compute the probability of P(-1.95 < z < 0.39)

a.         0.3227             b.         -0.3227            c.         -0.6261            d.         0.6261

26.  If z is a standard normal variable, compute the probability of P(-1.75 < z < -1.04)

a.         0.8107             b.         0.0401             c.         -0.1091            d.         0.1091

27. Given that z is a standard normal random variable, find the value of z if the area between 0 and z is 0.47.

a.         0.0199             b.         0.1587             c.         1.88                 d.         0.1808

28. Given that z is a standard normal random variable, find the value of z if the area to the left of z is 0.2

a.         0.84                 b.         -0. 84               c.         0.52                 d.         -0.52

29. Given that z is a standard normal random variable, find the value of z if the area to the right of z is 0.9.

Problem F.

The starting salaries of individuals having an MBA degree is normally distributed with a mean of $40,000 and a standard deviation of $10,000. 

ANSWER QUESTIONS  30 - 32 BELOW.

30.  What is the probability that a randomly selected individual with an MBA degree will get a starting salary greater than $30,000?

a.         0.3413             b.         0.1587             c.         -1.0                  d.         0.8413

31.  What is the probability that a randomly selected individual with an MBA degree will get a starting salary of less than $47,500?

a.         0.7734             b.         0.75                 c.         0.2734             d.         0.2266

32.  What percentage of MBAs will get starting salaries between $34,000 to $46,000?

Problem G:

The travel time for a college student traveling between her home and college is uniformly distributed between 40 and 100 minutes.  ANSWER QUESTIONS 33 THROUGH 35 BELOW.

33.  The probability that she will finish her trip in 64 minutes or more is:

a.         0.1                   b.         0.4                   c.         0.6                   d.         1.6

34.  The probability that she will finish her trip in less than 60 minutes is:

a.         0.33                 b.         0.67                 c.         0.02                 d.         0.5

35.  The expected travel time for her trip is:

a.         65 minutes                                b.         less than 40 minutes