Question 1

Given the data set: 10, 12, 15, 22, 22, 34, 42, what is the mean of the data? Use the formula $$\bar{x} = \frac{\sum x_i}{n}.$$

Accepted Answer

$$22.43$$

Question 2

For the same data set: 10, 12, 15, 22, 22, 34, 42, what is the range?

Accepted Answer

$$32$$

Question 3

What is the formula for the sample mean?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 4

Which of the following is the correct formula for the population standard deviation?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 5

A normal distribution has mean $$\mu = 40$$ and standard deviation $$\sigma = 4. $$According to the Empirical Rule, approximately what percentage of observations fall between $$32$$ and $$48$$?

Accepted Answer

$$99.7\%$$

Question 6

For the same normal distribution ($$\mu = 40$$, $$\sigma = 4$$), what is the Z-score for an observation of $$30$$?

Accepted Answer

$$-2.5$$

Question 7

Given a sample with mean $$\bar{x} = 800$$ and standard deviation $$s = 50$$, what is the Z-score for a rental rate of $$730$$?

Accepted Answer

$$-1.4$$

Question 8

In a data set of small SUV miles per gallon: 39, 31, 39, 35, 39, 29, 40, 43, 44, 44, 47, what is the interquartile range (IQR)?

Accepted Answer

$$9$$

Question 9

Which of the following best describes why the regression coefficients $$b_1$$ and $$b_2 in $$the equation $$y = 62.65 - 1.86x_1 - 0.52x_2$$ are negative?

Accepted Answer

Increasing insulation thickness or outdoor temperature is associated with decreased natural gas consumption.

Question 10

Using the regression equation $$y = 62.65 - 1.86x_1 - 0.52x_2$$, what is the expected monthly natural gas consumption if $$x_1 = 6$ inches and x_2$ = 40$$ degrees F?

Accepted Answer

$$31.37$$ cubic feet

Question 11

If a committee of 3 people is to be selected from a staff of 12, with one person as lead, one as record keeper, and one as scheduler, how many ways can this be done?

Accepted Answer

$$1320$$

Question 12

Given a normal distribution with mean $$\mu = 40$$ and standard deviation $$\sigma = 4$$, what is the data value $$x$$ corresponding to a Z-score of $$+1.5$$?

Accepted Answer

$$46$$

Question 13

Which of the following is the correct formula for the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 14

For a data set with mean $$\mu = 40$$ and standard deviation $$\sigma = 4$$, what percentage of observations are less than $$44$$ according to the Empirical Rule?

Accepted Answer

$$84\%$$

Question 15

A sample of apartment rental rates is approximately bell-shaped with mean $$800$$ and standard deviation $$50. $$What is the approximate probability that a rental rate is between $$750$$ and $$900$$?

Accepted Answer

$$81.5\%$$

Question 16

Given the data set: 10, 12, 15, 22, 22, 34, 42, what is the median?

Accepted Answer

$$22$$

Question 17

For the data set: 10, 12, 15, 22, 22, 34, 42, what is the mode?

Accepted Answer

$$22$$

Question 18

If the standard deviation of a data set is $$4$$, what is the variance?

Accepted Answer

$$16$$

Question 19

Which of the following best describes the Empirical Rule for a normal distribution?

Accepted Answer

Approximately $$68\% of $$data falls within $$1$$ standard deviation, $$95\%$$ within $$2$$, and $$99.7\%$$ within $$3$$ standard deviations of the mean.

Statistics Review: Measures, Boxplots, Empirical Rule, Regression, and Combinatorics

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