Statistics and Probability Answers

4.43 Three data entry specialists enter requisitions into a computer. Specialist 1 processes 30 percent of the requisitions, specialist 2 processes 45 percent, and specialist 3 processes 25 percent. The proportions of incorrectly entered requisitions by data entry specialists 1, 2, and 3 are .03, .05, and .02, respectively. Suppose that a random requisition is found to have been incorrectly entered. What is the probability that it was processed by data entry specialist 1? By data entry specialist 2? By data entry specialist 3?

4.29 A sprinkler system inside an office building has two types of activation devices, D1 and D2, which operate independently. When there is a fire, if either device operates correctly, the sprinkler system is turned on. In case of fire, the probability that D1 operates correctly is .95, and the probability that D2 operates correctly is .92. Find the probability that

a. Both D1 and D2 will operate correctly.

b. The sprinkler system will come on.

c. The sprinkler system will fail.

4.11... Of 10,000 students at a college, 2,500 have a Mastercard (M), 4,000 have a VISA (V), and 1,000 have both.

a. Find the probability that a randomly selected student

(1) Has a Mastercard.
(2) Has a VISA.
(3) Has both credit cards.

b. Construct and fill in a contingency table summarizing the credit card data. Employ the following pairs of events: M and _M , V and _ . ￣ V￣

c. Use the contingency table to find the probability that a randomly selected student

(1) Has a Mastercard or a VISA.
(2) Has neither credit card.
(3) Has exactly one of the two credit cards.

4.3 Two randomly selected grocery store patrons are each asked to take a blind taste test and to then state which of three diet colas (marked as A, B, or C) he or she prefers.

a. Draw a tree diagram depicting the sample space outcomes for the test results.

b. List the sample space outcomes that correspond to each of the following events:

(1) Both patrons prefer diet cola A.
(2) The two patrons prefer the same diet cola.
(3) The two patrons prefer different diet colas.
(4) Diet cola A is preferred by at least one of the two patrons.
(5) Neither of the patrons prefers diet cola C.

c. Assuming that all sample space outcomes are equally likely, find the probability of each of the events given in part b.

3.27 The Morningstar Top Fund lists at the Morningstar.com website give the mean yearly return and the standard deviation of the returns for each of the listed funds. As given by Morningstar.com on March 17, 2005, the RS Internet Age Fund has a mean yearly return of 10.93 percent with a standard deviation of 41.96 percent; the Franklin Income A fund has a mean yearly return of 13 percent with a standard deviation of 9.36 percent; the Jacob Internet fund has a mean yearly return of 34.45 percent with a standard deviation of 41.16 percent.

a. For each mutual fund, find an interval in which you would expect 95.44 percent of all yearly returns to fall. Assume returns are normally distributed.

b. Using the intervals you computed in part a, compare the three mutual funds with respect to average yearly returns and with respect to variability of returns.

c. Calculate the coefficient of variation for each mutual fund, and use your results to compare the funds with respect to risk. Which fund is riskier?

3.22 In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force.

$157 $132 $109 $145 $125 $139

a Calculate _ , s2 and s for the expense data. In addition, show that the two different formulas for calculating s2 give the same result.

b. Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force.

c. If a member of the sales force submits an entertainment expense (dinner cost for four) of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.

d. Compute and interpret the z-score for each of the six entertainment expenses.

3.19 Consider the following population of five numbers: 5, 8, 10, 12, 15. Calculate the range, variance, and standard deviation of this population.

2.47 Construct a cross-tabulation table using cola preference (Rola or Koka) as the row variable and the number of 12-packs consumed in a typical month (categories 0 through 5, 6 through 10, and more than 10) as the column variable. Based on the table, answer the following:

a. How many shoppers who preferred Rola-Cola in the blind taste test purchase 10 or fewer 12-packs of cola drinks in a typical month?

b. How many shoppers who preferred Koka-Cola in the blind taste test purchase 6 or more 12-packs of cola drinks in a typical month?

c. What kind of relationship, if any, seems to exist between cola preference and cola consumption in a typical month?

2.41 THE VIDEO GAME SATISFACTION RATING CASE

Recall that 65 purchasers have participated in a survey and have rated the XYZ-Box video game system. The composite ratings that have been obtained are as follows:

39 38 40 40 40 46 43 38 44 44 44
45 42 42 47 46 45 41 43 46 44 42
38 46 45 44 41 45 40 36 48 44 47
42 44 44 43 43 46 43 44 44 46 43
42 40 42 45 39 43 44 44 41 39 45
41 39 46 45 43 47 41 45 45 41

a. Construct a stem-and-leaf display for the 65 composite ratings. Hint: Each whole number rating can be written with an “implied tenth place” of zero. For instance, 39 can be written as 39.0. Use the implied zeros as the leaf values and the whole numbers 36, 37, 38, 39, etc. as the stem values.

b. Describe the distribution of composite ratings.

c. If we consider a purchaser to be “very satisfied” if his or her composite score is at least 42, can we say that almost all purchasers of the XYZ-Box video game system are “very satisfied”?

2.19 Recall that 60 randomly selected shoppers have rated a new bottle design for a popular soft drink. The data are given below.

34 33 33 29 26 33 28 25 32 33
32 25 27 33 22 27 32 33 32 29
24 30 20 34 31 32 30 35 33 31
32 28 30 31 31 33 29 27 34 31
31 28 33 31 32 28 26 29 32 34
32 30 34 32 30 30 32 31 29 33

a. Construct a relative frequency distribution and a percent frequency distribution for the bottle design ratings.

b. Construct a cumulative frequency distribution and a cumulative percent frequency distribution.

c. Draw a frequency ogive for the bottle design ratings.