Q: A contingency table shows the counts of music genre preferences by location. If 103 respondents chose Classical music and 31 of them are from the West, what percentage of Classical music listeners are from the West?

$$\frac{31}{103} \times 100 = 30.1\%$$

Q: A food truck’s daily profit is given by $$p = 5y - 200$$, where $$y is $$the number of meal combos sold. If the median number of combos sold is 95, what is the median daily profit?

$$p = 5 \times 95 - 200 = 475 - 200 = 275$$

Q: A bag of baby carrots has a mean weight of 16.3 ounces and a standard deviation of 0.3 ounces. What percentage of bags will contain at least 1 pound (16 ounces)?

$$z = \frac{16 - 16.3}{0.3} = -1$$, \text{so } P(X \geq 16) = 1 - P(Z \u003c -1) = 1 - 0.1587 = 0.8413 = 84.13\%$

Q: Lawyers want no more than 4% of carrot bags to weigh less than 16 ounces. If the mean is set at $$\mu$$ and the standard deviation is 0.3 ounces, what should $$\mu be$$?

$$P(X \u003c 16) = 0.04 \rightarrow z = -1.75$$, \mu = 16 - (-1.75 \times 0.3) = 16 + 0.525 = 16.525$

Q: Given the following summary statistics for a regression predicting Time (min) from Friends: $$\bar{x} = 21.61$$, $$\bar{y} = 105.13$$, $$s_x = 5.72$$, $$s_y = 39.91$$, $$r = 0.388. $$What is the slope estimate $$b_1$$?

$$b_1 = r$$ \frac{s_y}{s_x} = 0.388 \times \frac{39.91}{5.72} = 2.71$$

Question 1

A contingency table shows the counts of music genre preferences by location. If 103 respondents chose Classical music and 31 of them are from the West, what percentage of Classical music listeners are from the West?

Accepted Answer

$$\frac{31}{103} 	imes 100 = 30.1\%$$

Question 2

Given a five-number summary for daily meal combos served: Min = 32, $$Q_1 = 80$, Median = 95, Q_3$ = 110$$, Max = 153. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 110 - 80 = 30$$

Question 3

A food truck’s daily profit is given by $$p = 5y - 200$$, where $$y is $$the number of meal combos sold. If the median number of combos sold is 95, what is the median daily profit?

Accepted Answer

$$p = 5 	imes 95 - 200 = 475 - 200 = 275$$

Question 4

A histogram of sugar content in cereals is right-skewed. Which of the following is most likely true about the mean and median?

Accepted Answer

The mean is greater than the median.

Question 5

Children’s cereals have a higher median sugar content than adult cereals. Which group is likely to have greater variability in sugar content?

Accepted Answer

Children’s cereals, because their boxplot shows a larger spread.

Question 6

Old Forge, NY, had a low temperature of $$-36^{\circ}F ($$mean $$4^{\circ}F$$, SD $$10^{\circ}F). $$Taboko, TX, had a high of $$116^{\circ}F ($$mean $$91^{\circ}F$$, SD $$7^{\circ}F). $$Which event was more unusual?

Accepted Answer

Old Forge, NY, because its z-score is lower.

Question 7

A bag of baby carrots has a mean weight of 16.3 ounces and a standard deviation of 0.3 ounces. What percentage of bags will contain at least 1 pound (16 ounces)?

Accepted Answer

$$z = \frac{16 - 16.3}{0.3} = -1$$, 	ext{so } P(X \geq 16) = 1 - P(Z \u003c -1) = 1 - 0.1587 = 0.8413 = 84.13\%$

Question 8

Lawyers want no more than 4% of carrot bags to weigh less than 16 ounces. If the mean is set at $$\mu$$ and the standard deviation is 0.3 ounces, what should $$\mu be$$?

Accepted Answer

$$P(X \u003c 16) = 0.04 ightarrow z = -1.75$$, \mu = 16 - (-1.75 	imes 0.3) = 16 + 0.525 = 16.525$

Question 9

A company president wants only 4% of carrot bags to weigh less than 16 ounces, with the mean at 16.3 ounces. What standard deviation should the machine achieve?

Accepted Answer

$$z = \frac{16 - 16.3}{\sigma} = -1.75 \rightarrow \sigma = \frac{16.3 - 16}{1.75} = 0.171$$

Question 10

A scatterplot shows a strong positive linear association between waist size and body fat percentage. Which value is most likely the correlation coefficient?

Accepted Answer

$$r = 0.81$$

Question 11

Given the following summary statistics for a regression predicting Time (min) from Friends: $$\bar{x} = 21.61$$, $$\bar{y} = 105.13$$, $$s_x = 5.72$$, $$s_y = 39.91$$, $$r = 0.388. $$What is the slope estimate $$b_1$$?

Accepted Answer

$$b_1 = r$$ \frac{s_y}{s_x} = 0.388 	imes \frac{39.91}{5.72} = 2.71$$

Question 12

What percentage of the variability in Time can be explained by Friends, given $$r = 0.388$$?

Accepted Answer

$$r^2$$ = $$(0.388)^2 = 0.150 = 15.0$$\%$$

Question 13

Given the regression equation $$\hat{y} = b_0$ + b_1x$$, and $$b_1 = 2.71$, $$\bar{x} = 21.61$$, $$\bar{y} = 105.13$$, what is the y$-intercept b_0$?

Accepted Answer

$$b_0$$ = \bar{y} - $$b_1$$ \bar{x} = 105.13 - 2.71 	imes 21.61 = 46.47$$

Question 14

For the data $$x = [2, 3, 4]$$, $$y = [5, 9, 7]$$, what is the correlation coefficient $$r$$?

Accepted Answer

$$r = 0.5$$

Question 15

Which of the following best describes the conditional distribution of Genre for the 'South' location, given the counts: Classical 27, Country 93, Pop Rock 52, Total 172?

Accepted Answer

Classical: $$\frac{27}{172} \approx 15.7\%$$, Country: $$\frac{93}{172} \approx 54.1\%$$, Pop Rock: $$\frac{52}{172} \approx 30.2\%$$

Question 16

If the median sugar content of cereals is 18.4%, which of the following could be the mean sugar content if the distribution is right-skewed?

Accepted Answer

24.9%

Statistics Exam Study Guide: Descriptive Statistics, Probability, and Regression

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