an area .05 to the left of z

4.68 Find the probability of observing a value of z greater than these values. a. 1.96

b. 2.21 c. ⫺2.86

d. ⫺0.73

Gov. 4.69 Records maintained by the office of budget in a particular state indicate that the amount of time elapsed between the submission of travel vouchers and the final reimbursement of funds has approximately a normal distribution with a mean of 39 days and a standard deviation of 6 days.

a. What is the probability that the elapsed time between submission and reimbursement

will exceed 50 days?

b. If you had a travel voucher submitted more than 55 days ago, what might you

conclude? Edu. 4.70 The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. What percentage of the scores can be expected to satisfy each condition?

a. Greater than 600 b. Greater than 700

c. Less than 450 d. Between 450 and 600

Bus. 4.71 Monthly sales figures for a particular food industry tend to be normally distributed with mean of 150 thousand dollars and a standard deviation of 35 thousand dollars. Compute the following probabilities:

a. Py ⬍ 200 b. Py ⬎ 100

c. P100 ⬍ y ⬍ 200 4.72 Refer to Exercise 4.70. An exclusive club wishes to invite those scoring in the top 10 on the College Boards to join. a. What score is required to be invited to join the club? b. What score separates the top 60 of the population from the bottom 40? What do we call this value? 4.11 Random Sampling Soc. 4.73 City officials want to sample the opinions of the homeowners in a community regarding the desirability of increasing local taxes to improve the quality of the public schools. If a random number table is used to identify the homes to be sampled and a home is discarded if the home- owner is not home when visited by the interviewer, is it likely this process will approximate random sampling? Explain. Pol. 4.74 A local TV network wants to run an informal survey of individuals who exit from a local vot- ing station to ascertain early results on a proposal to raise funds to move the city-owned historical museum to a new location. How might the network sample voters to approximate random sampling? Psy. 4.75 A psychologist is interested in studying women who are in the process of obtaining a divorce to determine whether the women experienced significant attitudinal changes after the divorce has been finalized. Existing records from the geographic area in question show that 798 couples have recently filed for divorce. Assume that a sample of 25 women is needed for the study, and use Table 13 in the Appendix to determine which women should be asked to participate in the study. Hint: Begin in column 2, row 1, and proceed down. Pol. 4.76 Suppose you have been asked to run a public opinion poll related to an upcoming election. There are 230 precincts in the city, and you need to randomly select 50 registered voters from each precinct. Suppose that each precinct has 1,000 registered voters and it is possible to obtain a list of these persons. You assign the numbers 1 to 1,000 to the 1,000 people on each list, with 1 to the first person on the list and 1,000 to the last person. You need to next obtain a random sample of 50 numbers from the numbers 1 to 1,000. The names on the sampling frame corresponding to these 50 numbers will be the 50 persons selected for the poll. A Minitab program is shown here for purposes of illustration. Note that you would need to run this program 230 separate times to obtain a new random sample for each of the 230 precincts. Follow these steps: Click on Calc. Click on Random Data. Click on Integer. Type 5 in the Generate rows of data box. Type c1– c10 in the Store in Columns: box. Type 1 in the Minimum value: box. Type 1000 in the Maximum value: box. Click on OK. Click on File. Click on Print Worksheet.

a. Using either a random number table or a computer program, generate a second ran-

dom sample of 50 numbers from the numbers 1 to 1,000.

b. Give several reasons why you need to generate a different set of random numbers for

each of the precincts. Why not use the same set of 50 numbers for all 230 precincts? 4.12 Sampling Distributions 4.77 A random sample of 16 measurements is drawn from a population with a mean of 60 and a standard deviation of 5. Describe the sampling distribution of , the sample mean. Within what interval would you expect to lie approximately 95 of the time?

4.78 Refer to Exercise 4.77. Describe the sampling distribution for the sample sum . Is it un-

likely improbable that would be more than 70 units away from 960? Explain. Psy. 4.79 Psychomotor retardation scores for a large group of manic-depressive patients were approximately normal, with a mean of 930 and a standard deviation of 130. a. What fraction of the patients scored between 800 and 1,100? b. Less than 800? c. Greater than 1,200? Soc. 4.80 Federal resources have been tentatively approved for the construction of an outpatient clinic. In order to design a facility that will handle patient load requirements and stay within a lim- ited budget, the designers studied patient demand. From studying a similar facility in the area, they found that the distribution of the number of patients requiring hospitalization during a week could be approximated by a normal distribution with a mean of 125 and a standard deviation of 32.

a. Use the Empirical Rule to describe the distribution of y, the number of patients

requesting service in a week.

b. If the facility was built with a 160-patient capacity, what fraction of the weeks might

the clinic be unable to handle the demand? a y i a y i y y C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 340 701 684 393 313 312 834 596 321 739 2 783 877 724 498 315 282 175 611 725 571 3 862 625 971 30 766 256 40 158 444 546 4 974 402 768 593 980 536 483 244 51 201 5 232 742 1 861 335 129 409 724 340 218