2843 ECON 010 Exam 1 Spring 2006 Form A
Name ID # Lab Instructor Lab Meeting Time
KEY
Students must show all work on problems that involve calculation.
Questions 1 through 4 refer to the following. Gas mileages for cars owned by a corporation are surveyed. The relative frequency distribution by miles per gallon (MPG) for the 20 cars in this population is shown in the table below. MPG 6 up to 12 12 up to 18 18 up to 24 24 up to 30 1. relative frequency .10 .25 .45 .20
What is the median class? a. b. c. d. 6 up to 12 12 up to 18 18 up to 24 24 up to 30
*
2.
Calculate the mean gas mileage in MPG for these cars. (Hint: As a check figure, the answer is equal to the tetrahedral constant, t.)
19.5
3.
What is the cumulative frequency of the class 12 up to 18?
7
4.
Calculate the standard deviation. a. b. c. d. 5.3245 * 5.4628 28.35 29.8241
1
5.
Suppose P(A) = .60 and P(B) = .50. Is it possible for P(A | B), i.e., the conditional probability of A given B, to equal the probability that both A and B occur? a. b. c. d. Yes, if A and B are statistically independent. Yes, if A and B are mutually exclusive. Yes, if A and B are collectively exhaustive. No, this is impossible. *
Questions 6 10 refer to the following: A large corporation conducted a study of its overseas workforce. It found that 77% of its workers were married. Among its single workers, 25% left within a year whereas only 14% of the married workers left within a year.
6.
What is the probability that a worker will stay longer than a year?
_______.8347____________________________
7.
When a worker has served the company for more than a year, what is the probability that he/she is married? a. b. c. d. e. 10.8%% 23% 66.22% 79.33% 83.47%
*
2
8.
What is the probability that a randomly selected person will be single and will leave the company within the first year?
____________.0575_______________________
9.
Show whether marital status and length of employment are independent?
0.6622
0.642719
so, no
___________________________________
10.
If workers married have an average annual salary of $25,920 and a standard deviation of $1,296, than according to the rule of thumb (empirical rule), there is 95% probability that a randomly selected worker will have a salary that lies between what two numbers?
____$23,328_____________
_
$28,512
3
Questions 11 15 refer to the following: A large nationwide chain of home improvement centers is having an end-of-season clearance on tractors. The number of John Deere tractors sold during this sale at a sample of 10 stores is as follows: 8, 12, 2, 4, 7, 8, 10, 5, 8, 12
11.
Calculate the arithmetic mean. a. b. c. d. 6.78 7.6 9.13 10.0 *
12.
What is the sample standard deviation?
3.278
13.
If one of the stores from the sample is selected at random, what is the probability that its sales will be greater than the mode?
.3
14.
If one of the stores from the sample is randomly selected, what is the probability that it will lie between the first and third quartiles (i.e., it will be greater than the first quartile but less than the third quartile)?
.4
4
15.
The IRS reported that 5.5% of all tax payers filling out the 1040EZ short form make mistakes. If 20 of these forms are chosen at random, what is the probability that more than 2 of them will contain errors?
.094320529 __________________________
Questions 16 18 refer to the following. A factory manager is considering whether to replace a temperamental copy machine. A review of past records indicates the following probability distribution of the X, the number of breakdowns, in a week. Number of breakdowns (X) Probability 0 .10 1 .26 2 .42 3 .16 4 .06
The weekly dollar cost (C) of the breakdowns can be expressed as C = 100 + 75X.
16.
What is the expected value of the number of weekly breakdowns?
1.82 __________________________
17.
What is the variance of the cost of the breakdowns?
5,780.25 __________________________
5
18.
What is the coefficient of variation of the cost of the breakdowns?
32.15% __________________________
6