Less than 450 d. Between 450 and 600

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