business statistics midterm

Question 1

The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy.

City	Hi	Lo	Condition
Acapulco	99	77	pc
Bangkok	92	78	pc
Mexico City	77	57	sh
Montreal	72	56	pc
Paris	77	58	c
Rome	88	68	cl

1. Is “Montreal” an element, variable, or observation?

2. Provide the observation for Rome.

3. Give an example of a categorical variable.

4. Provide the ranges for low and high temperatures.

Question 2

A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.

D	B	C	D
A	B	F	A
A	C	B	B
B	C	B	D
A	B	C	A

5. Develop a frequency distribution for her grades.

6. Develop an appropriated titled and labeled bar chart for her grades.

7. Construct a pie chart for her grades.

8. Explain a situation in which the bar chart would be better to show this information than a pie chart.

Question 3

The number of hours worked per week for a sample of ten students is shown below.

Student	Hours
1	17
2	40
3	6
4	19
5	6
6	24
7	32
8	6
9	8
10	30

9. Determine the mean, median, and mode.

10. Explain which of the three values (mean, median, mode) is the best representation of central tendency.

11. What is the standard deviation for the number of hours worked? What does standard deviation tell us?

Question 4

You are given the following information on Events A, B, C, and D.

P(A) = .5

P(B) = .3

P (C) = .15

P(A U D) = .7

P(A ∩ C) = 0.05

P (A │B) = 0.22

P (A ∩ D) = 0.25

12. Compute P(D).

13. Compute P(A ∩ B).

14. Compute P(A | C).

15. Compute the probability of the complement of C.

16. What does it mean to be mutually exclusive? Give an example of two events that are mutually exclusive.

Question 5

When a particular machine is functioning properly, 75% of the items produced are non-defective.

17. If eight items are examined, what is the probability that one is defective?

18. If eight items are examined, what is the probability that exactly three are non-defective?

19. If eight items are examined, what is the probability that at least 6 are non-defective?

Question 6

The average starting salary of this year’s graduates of a large university (LU) is $55,000 with a standard deviation of $4,000. Furthermore, it is known that the starting salaries are normally distributed.

20. What is the probability that a randomly selected LU graduate will have a starting salary of at least $52,700?

21. Individuals with starting salaries of less than $45,00 receive a free class. What percentage of the graduates will receive the free class?

22. What percent of graduates will have their salaries one standard deviation from the mean?

23. What is the range of salaries that are one standard deviation from the mean?

Question 7

A simple random sample of 6 computer programmers in Houston, Texas revealed the sex of the programmers and the following information about their weekly incomes.

Programmer	Weekly Income	Sex
A	$250	M
B	$270	M
C	$285	F
D	$240	M
E	$255	M
F	$290	F

24. If all the salaries were written on separate pieces of paper, and one was drawn at random, what is the probability that the one that was drawn would be over $252?

25. If a programmer were selected at random to complete a project, what would the probability be that the programmer was male?

26. What is the probability of selecting a male programmer whose weekly income is over $260?

Question 8

Students of a large university spend an average of $6 a day on lunch. The standard deviation of the expenditure is $1.

27. What is the probability that the sample mean will be at least $4.50?

28. What is the probability that the sample mean will be $7.90?

29. Doria spent $2.99 on her lunch on Friday. Explain to her, in terms of standard deviation, why this is not a typical expenditure at this campus.