BMA 140 WINTER 2011 PRACTICE (Midterm) 1. Monthly rent data in dollars for a sample of 10 one-bedroom apartments in a small town in Iowa are given below: 220 216 220 205 210 240 195 235 204 250 a. Compute the sample monthly average rent b. Compute the sample median c. What is the mode? d. Describe briefly what each statistic in parts a. to c. tells you about the data. 2. Suppose that a firm’s sales were $2,500,000 four years ago, and sales have grown annually by 25%, 15%, -5%, and 10% since that time. What was the geometric mean growth rate in sales over the past four years? . Suppose that a firm’s sales were $3,750,000 five years ago and are $5,250,000 today. What was the geometric mean growth rate in sales over the past five years? 4. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30. Compute the following measures of central location and variability: a. mean b. median c. standard deviation d. coefficient of variation 5. The annual percentage rates of return over the past 10 years for two mutual funds are as follows: Fund A: 7. 1 -7. 4 19. 7 -3. 9 32. 4 41. 7 23. 2 4. 0 1. 29. 3 Fund B: 10. 8 -4. 1 5. 1 10. 9 26. 5 24. 0 16. 9 9. 4 -2. 6 10. 1 Which fund would you classify as having the higher level of risk? 6. A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of six cartons. a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61? b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean? c.

If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand? 7. A sample of 12 measurements has a mean of 25 and a standard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having common value of 25 each. a. Find the mean of the sample of 14 measurements. b. Find the standard deviation of the sample of 14 measurements. 8. Given the following sample data x| 420| 610| 625| 500| 400| 450| 550| 650| 480| 565| y| 2. 80| 3. 60| 3. 75| 3. 00| 2. 50| 2. 0| 3. 50| 3. 90| 2. 95| 3. 30| a. Calculate the covariance and the correlation coefficient. b. Comment on the relationship between x and y. c. Draw the scatter diagram and plot the least squares line. 9. A Ph. D. graduate has applied for a job with two universities: A and B. The graduate feels that she has a 60% chance of receiving an offer from university A and a 50% chance of receiving an offer from university B. If she receives an offer from university B, she believes that she has an 80% chance of receiving an offer from university A. a. What is the probability that both universities will make her an offer? . What is the probability that at least one university will make her an offer? c. If she receives an offer from university B, what is the probability that she will not receive an offer from university A? 10. There are three approaches to determining the probability that an outcome will occur: classical, relative frequency, and subjective. Which is most appropriate in determining the probability of the following outcomes? a. The unemployment rate will rise next month. b. Five tosses of a coin will result in exactly two heads. c. An American will win the French Open Tennis Tournament in the year 2000. . A randomly selected woman will suffer a breast cancer during the coming year. 11. At the beginning of each year, an investment newsletter predicts whether or not the stock market will rise over the coming year. Historical evidence reveals that there is a 75% chance that the stock market will rise in any given year. The newsletter has predicted a rise for 80% of the years when the market actually rose, and has predicted a rise for 40% of the years when the market fell. Find the probability that the newsletter’s prediction for next year will be correct. 12. Suppose P() = 0. 30, P() = 0. 0, and P() = 0. 50. a. Find P(A and B). b. Find P() c. Find P(A or B). 13. A standard admissions test was given at three locations. One thousand students took the test at location A, 600 students at location B, and 400 students at location C. The percentages of students from locations A, B, and C, who passed the test were 70%, 68%, and 77%, respectively. One student is selected at random from among those who took the test. a. What is the probability that the selected student passed the test? b. If the selected student passed the test, what is the probability that the student took the test at location B? . What is the probability that the selected student took the test at location C and failed? 14. Sales records of an appliance store showed the following number of dishwashers sold weekly for each of the last 50 weeks. Number of Dishwashers Sold| Number of Weeks| 0| 20| 1| 15| 2| 10| 3| 4| 4| 1| a. Define the random experiment of interest to the store. b. List the outcomes in the sample space c. Assign probabilities to the outcomes. d. What approach have you used in determining the probabilities in part (c)? e. What is the probability of selling at least two dishwashers in any given week? 15.

Suppose A and B are two mutually exclusive events for which P(A) = 0. 30 and P(B) = 0. 40. a. Find P(A and B). b. Find P(A or B). c. Are A and B independent events? Explain using probabilities. 16. Is it possible to have two events for which P(A) = 0. 40, P(B) = 0. 50, and P(A or B) = 0. 30? Explain. 17. A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1% of the population. The firm has announced that 95% of those infected will show a positive test result, while 98% of those not infected will show a negative test result. What proportion of test results are correct? 18.

An accounting firm has recently recruited five graduates: two men and three women. Two of the graduates are to be selected at random to work in the firm’s suburban office. a. What is the probability that two women will be selected? b. What is the probability that at least one woman will be selected? 19. An insurance company has collected the following data on the gender and marital status of 300 customers. Marital Status Gender| Single| Married| Divorced| Male| 25| 125| 30| Female| 50| 50| 20| Suppose that a customer is selected at random. Find the probability that the customer selected is: a. a married female b. ot single c. married if the customer is male d. female or divorced e. Are gender and marital status mutually exclusive? Explain using probabilities. f. Is marital status independent of gender? Explain using probabilities. 1. ANSWERS: a. $219. 50 b. $218 c. $220 d. The average monthly rate is $219. 50, with half of the cases being less than $218. The most common value found was $220. 2. ANSWER: If is the geometric mean, then = (1+0. 25)(1+0. 15)(1-0. 05)(1+0. 10)=1. 5022 0. 1071 or 10. 71% 3. ANSWER: If is the geometric mean, then 3,750,000 = 5,250,000 = 0. 0696 or 6. 96% 4. ANSWERS: a. 23. 714 b. median = 22. c. 5. 499 d. cv = 0. 232 5. ANSWER: Variance of returns will be used as the measure of risk of an investment. Since, and, fund A has the higher level of risk. 6. ANSWERS: a. Approximately 68% b. Approximately 5% c. Almost never, because the value 77 is 3. 66 standard deviations above the mean 7. a. 25 b. 3. 679 8. = = 41. 25 a. There is a very strong positive linear relationship between X and Y. c. 9. ANSWERS: a. 0. 4 b. 0. 7 c. 0. 2 10. ANSWERS: a. subjective b. classical c. subjective d. relative frequency 11. ANSWER: 0. 75 12. ANSWERS: a. 0. 42 b. 0. 43 c. 0. 85 13. ANSWERS a. 0. 708 b. 0. 288 c. 0. 046 14.

ANSWERS: a. The random experiment consists of observing the number of dishwashers sold in any given week. b. S = {0, 1, 2, 3, 4} c. Outcome| Prob. | 0| 0. 40| 1| 0. 30| 2| 0. 20| 3| 0. 08| 4| 0. 02| d. The relative frequency approach was used. e. P{2, 3, 4} = 0. 30 15. ANSWERS: a. 0. 00 b. 0. 70 c. No, since P(A and B) = 0. 00 P(A ). P(B) = 0. 12. 16. ANSWER: No, since P(A or B) must be at least as large as P(B). 17. ANSWER:0. 9797 18. ANSWERS: a. 0. 30 b. 0. 90 19. ANSWERS: a. 0. 167 b. 0. 75 c. 0. 694 d. 0. 50 e. No, since P(female and married) = 0. 167 > 0. No, since P(married / male) = 0. 694 P(married) = 0. 583