Question

You are asked to do a study of shelters for abused and battered women to determine the

necessary capacity I your city to provide housing for most of these women. After recording data

for a whole year, you find that the

mean number

of women in shelters each night is

250

, with a

standard deviation of 75

. Fortunately, the distribution of the number of women in the shelters

each night is normal, so you can answer the following questions posed by the city council.

a. If the city’s shelters have a capacity of

350

, will that be enough places for abused women

on

95%

of all nights? If not, what number of shelter openings will be needed?

b. The current capacity is only

220

openings, because some shelters have been closed. What

is the

percentage of nights

that the number of abused women seeking shelter will exceed

current capacity?

Homework Assignment 5

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2

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2. A criminologist developed a test to measure recidivism, where low scores indicated a lower

probability of repeating the undesirable behavior. The test is normed so that it has

a mean

of

140

and a

standard deviation of 40

.

a. What is the percentile rank of a score of 172?

b. What is the Z score for a test score of 200?

c. What percentage of scores falls between 100 and 160?

d. Suppose an individual is the 67

th

percentile in this test, what is his or her corresponding

recidivism score?

Homework Assignment 5

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3. We’ll examine the results of the 2014-2015 SAT math exam with a mean of 501 and standard

deviation of 117, as reported in Table 5.1.

Table 5.1 2014-2015 SAT Component Means and Standard Deviations for High School

Seniors

Critical Reading

Mathematics

Writing

Number of Test

Takers

Mean

Standard

Deviation

Mean

Standard

Deviation

Mean

Standard

Deviation

1,108,165

485

110

501

117

475

109

Source: College Board, 2015 College-Bound Seniors Total Group Profile Report, Table 3,

2015. The College Board.

www.collegeboard.org

Page 131 in Frankfort-Nachamias

a. What percentage of seniors scored

lower

than

300

on the math SAT?

b. What percentage scored

between 600 and 700

points?

Homework Assignment 5

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4. The number of hours people work each week varies widely for many reasons. Using the GSS

2014, you find that the

mean

number of hours worked last week was

41.47

, with a

standard

deviation of 15.04 hours

, based on a sample size of

895

.

a. Assume that hours worked is approximately normally distributed in the sample. What is

the probability that someone in the sample with work

60 hours or more

in a week?

b. What is the probability that someone will work

30 hours or fewer

in a week (i.e., work

part time)?

c. How many people (working part-time) does this represent in the sample?

d. What number of hours worked per week corresponds to the 60

th

percentile?

Homework Assignment 5

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5

of

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Chapter 6

6. An upper-level sociology class has

120

registered students: 34 seniors, 57 juniors, 22

sophomores, and 7 freshmen.

a. Imagine that you choose one random student from the classroom (perhaps by using a

random number table). What is the probability that the student will be a

junior?

b. What is the probability that the student will be a

freshman

?

Annotations

Answer 1