Suppose that all the values in a data set are converted to z-scores. Which of the statements below istrue?

The mean of the z-scores will be 0, and the standard deviation of the z-scores will be 1.

Find all measures of center: A store manager kept track of the number of newspapers sold each week over a randomly selected seven-week period. The results are shown below.

80 39 214 152 264 239 232

Find the median number of newspapers sold.

Mean: x̄ = 174.3 newspapers

Median: x(~) = 214.0 newspapers

Midrange: 151.5

Mode: none

Which is better:

A score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of 82 on a test with a mean of 75 and a standard deviation of 4?

The second 82

(82 – 70) ÷ 8 (82 – 75) ÷ 4

= 1.5 = 1.75

A department store, on average, has daily sales of $29,876.76. The standard deviation of sales is $1000.On Tuesday, the store sold $34,893.71 worth of goods.

Find Tuesday's z score.

Was Tuesday an unusually good day?

5.02, yes

(34,893.71 – 29,876.76) ÷ 1000

= 5.01695

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results: When investigating times required for drive-through service, the following results (in seconds) were obtained.

Restaurant A: 44 sec; s² = 260.8 sec²; s = 16.1 sec

Restaurant B: 46 sec; s² = 285.6 sec²; s = 16.9 sec

There is more variation in the times for restaurant B.

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.

A time for the 100 meter sprint of 21.3 seconds at a school where the mean time for the 100 meter sprint is 17.5 seconds and the standard deviation is 2.1 seconds.

1.80; not unusual

(21.3 – 17.5) ÷ 2.1

= 1.80952381

Use the given sample data to find Q3:

49 52 52 52 74 67 55 55

61.0

The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below.

Construct a boxplot for the data set.

310 320 450 460 470 500 520 540

580 600 650 700 710 840 870 900

1000 1200 1250 1300 1400 1720 2500 3700

The​ 5-number summary is 310​, 510​, 705​, 1225, 3700

The heights of a group of professional basketball players are summarized in the frequency distribution below.

Find the mean height.

x̄ = 76.7 in.

(Use calculator)

L1 L2

midpt freq

1–Var Stats L1,L2

mean = 76.68867925

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

95%

(96 – 120) ÷ 12 (144 – 120) ÷ 12

= -2SD = 2SD

2SD = 95%