##### General Statistics: Ch 3 Test

College: First year, College: Second year, College: Third year, College: Fourth year

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; s^{2 }= 260.8 sec^{2}; s = 16.1 sec

Restaurant B: 46 sec; s^{2 }= 285.6 sec^{2}; 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%*