Question 1

A variable x has a mean, µ, of 22 and a standard deviation, Ϭ, of 7. Determine the standardized version of x.

Accepted Answer

The standardized version of a variable, often denoted as $z$, is calculated by subtracting the mean ($\mu$) from the variable ($x$) and then dividing by the standard deviation ($\sigma$). Therefore, the correct formula is $z = \frac{x - \mu}{\sigma}$, which matches option B: $z = \frac{x - 22}{7}$.

Question 2

Find the median for the given sample data.
-6, 7, 23, 21, 30, 46

Accepted Answer

The answer of Find the median for the given sample...

Question 3

The normal annual precipitation (in inches)is given below for 21 different U.S. cities. 
$\begin{array} { l l l l l l l } 39.1 & 32.8 & 18.5 & 35.2 & 27.1 & 27.8 & 8.6 \end{array}$
$\begin{array} { l l l l l r r } 23.4 & 42.6 & 34.7 & 20.4 & 12.0 & 5.1 & 14.3 \end{array}$
$\begin{array} { l l l l l l l } 22.5 & 10.9 & 15.9 & 25.4 & 17.2 & 14.6 & 51.7 \end{array}$

Accepted Answer

The answer of The normal annual precipitation (in inches)is given...

Question 4

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations.
-Let $x _ { 1 } = 12 , x _ { 2 } = 17 , x _ { 3 } = 5 , x _ { 4 } = 1$, and $x _ { 5 } = 7$. Determine $\bar { x }$.

Accepted Answer

$\bar { x }$ is the mean of the given values. To find it, add all the values together and divide by the number of values: $\bar { x } = \frac { 12 + 17 + 5 + 1 + 7 } { 5 } = \frac { 42 } { 5 } = 8.4$.

Question 5

Construct and interpret a boxplot or a modified boxplot as specified.
-The weights (in pounds)of 30 newborn babies are listed below. Construct a boxplot for the data. $\begin{array} { l l l l l l l l l l } 5.5 & 5.7 & 5.8 & 5.9 & 6.1 & 6.1 & 6.3 & 6.4 & 6.5 & 6.6 \ 6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \ 7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7 \end{array}$

Accepted Answer

The answer of Construct and interpret a boxplot or a...

Question 6

Identify potential outliers, if any, for the given data.
-The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below. 
$\begin{array} { r r r r r r r r } 310 & 320 & 450 & 460 & 470 & 500 & 520 & 540 \ 580 & 600 & 650 & 700 & 710 & 840 & 870 & 900 \ 1000 & 1200 & 1250 & 1300 & 1400 & 1720 & 2500 & 3700 \end{array}$

Accepted Answer

The values 2500 and 3700 are significantly higher than the rest of the data, indicating they are potential outliers.

Question 7

Obtain the population standard deviation, Ϭ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the Observations. The normal annual precipitation (in inches)is given below for 8 different U.S. cities. 
$\begin{array} { l l l l } 6.7 & 8.3 & 5.7 & 14.2 \end{array}$
$\begin{array} { r r r r } 15.2 & 13.7 & 17.0 & 14.3 \end{array}$

Accepted Answer

The population standard deviation is 4.03 in.

Question 8

Find the mode(s)for the given sample data.
-The weights (in ounces)of 14 different apples are shown below. $\begin{array} { l l l l l l l } 5.4 & 4.3 & 4.6 & 5.8 & 4.0 & 5.4 & 4.3 \end{array}$
$\begin{array} { l l l l l l l } 5.3 & 5.6 & 5.8 & 5.4 & 5.3 & 5.8 & 6.3 \end{array}$

Accepted Answer

The mode is the value(s) that appears most frequently in a data set. Here, both 5.4 oz and 5.8 oz appear three times, making them the modes.

Question 9

Construct and interpret a boxplot or a modified boxplot as specified.
-The test scores of 40 students are listed below. Construct a boxplot for the data. $\begin{array} { l l l l l l l l l l } 25 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \end{array}$
$\begin{array} { l l l l l l l l l l } 59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 71 \end{array}$
$\begin{array} { l l l l l l l l l l l } 73 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \end{array}$
$\begin{array} { l l l l l l l l l l } 81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98 \end{array}$

Accepted Answer

The answer of Construct and interpret a boxplot or a...

Question 10

Find the median for the given sample data.
-The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. $\begin{array} { l l l l } 28 & 30 & 28 & 31 \end{array}$
$\begin{array} { l l l l } 31 & 28 & 33 & 30 \end{array}$
$\begin{array} { l l l l } 38 & 34 & 34 & 32 \end{array}$
$ \begin{array}{llll}27 & 34 & 28 & 23\end{array} $
$ \begin{array}{llll}18 & 30 & 30 & 30\end{array} $

Accepted Answer

First, arrange the data in ascending order: 18, 23, 27, 28, 28, 28, 30, 30, 30, 30, 31, 31, 32, 33, 34, 34, 38. The median is the middle number, which is 30 vehicles since there are an odd number of data points (17).

Question 11

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations.
-A sample of non-recyclable waste shipping companies in a certain state yielded the following amounts, in tons, of waste shipped during 2005. Determine $n , \sum \mathrm { x } _ { i }$, and $\bar { x }$.
$\begin{array}{rrrr}
1662 & 480 & 877 & 789 \
852 & 1770 & 592 & 1262 \
421 & 612 & 769 & 826
\end{array}$

Accepted Answer

The correct values are $n=12$ (total number of observations), $\sum x_i=10,912$ (sum of all observations), and $\bar{x}=909.3$ (average of observations, calculated as $\frac{10,912}{12}$).

Question 12

Determine the quartile or interquartile range as specified.
-The weekly salaries (in dollars)of sixteen government workers are listed below. Find the first quartile, 
$Q _ { 1 }$
$\begin{array} { l l l l } 690 & 598 & 813 & 659 \ 728 & 557 & 477 & 639 \ 526 & 669 & 685 & 464 \ 545 & 787 & 511 & 826 \end{array}$

Accepted Answer

The answer of Determine the quartile or interquartile range as...

Question 13

To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $\begin{array} { l l l l l l l l } \$ 410 & \$ 377 & \$ 395 & \$ 114 & \$ 293 & \$ 169 & \$ 140 & \$ 224 \end{array}$

Accepted Answer

The answer of To get the best deal on a...

Question 14

Identify potential outliers, if any, for the given data.
-The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. 
$\begin{array} { l l l l l } 0.4 & 1.0 & 1.5 & 1.6 & 2.0 \end{array}$
$\begin{array} { l l l l l } 2.2 & 2.4 & 2.7 & 3.4 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.5 & 3.6 & 3.6 & 3.7 & 3.7 \end{array}$
$\begin{array} { l l l l l } 3.9 & 4.1 & 4.2 & 4.2 & 7.0 \end{array}$

Accepted Answer

To identify outliers, we typically calculate the interquartile range (IQR) and then determine if any values fall more than 1.5*IQR below the first quartile or above the third quartile. In this dataset, the value 7.0 stands out as significantly higher than the rest, suggesting it could be an outlier. The value 0.4, while low, does not seem as dramatically separated from the other low values as 7.0 does from the high values. Without calculating the exact IQR and thresholds for outliers, the presence of 7.0 as a potential outlier is more apparent due to its significant deviation from the rest of the data.

Question 15

Use the empirical rule to solve the problem.
-The amount of Jen's monthly phone bill has a roughly bell-shaped distribution with a mean of $57 and a standard deviation of $9. What percentage of her phone bills are between $30 and $84?

Accepted Answer

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Here, $30 to $84 is $27 below and above the mean ($57), which is three standard deviations ($9 x 3 = $27). Therefore, about 99.7% of her phone bills fall within this range.

Question 16

Obtain the five-number summary for the given data.
2, 3, 5, 8, 10

Accepted Answer

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. For the data set 2, 3, 5, 8, 10, these are 2, 3, 5, 8, and 10, respectively.

Question 17

Identify potential outliers, if any, for the given data.
-The normal annual precipitation (in inches)is given below for 21 different U.S. cities. 
$\begin{array} { l l l l l l l } 32.4 & 30.3 & 34.6 & 65.6 & 22.1 & 31.8 & 16.6 \end{array}$
$\begin{array} { l l l l l l l } 28.0 & 36.2 & 59.4 & 25.5 & 47.2 & 45.6 & 8.3 \end{array}$
$\begin{array} { l l l l l l l l } 27.4 & 18.9 & 13.0 & 31.4 & 24.2 & 11.8 & 35.4 \end{array}$

Accepted Answer

The answer of Identify potential outliers, if any, for the...

Question 18

Find the range for the given data set.
-Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores.
21 35 20 48 58

Accepted Answer

The range of a set of data is the difference between the highest and lowest values. For Rich Borne's scores (21, 35, 20, 48, 58), the highest score is 58 and the lowest score is 20. Therefore, the range is 58 - 20 = 38.

Question 19

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Accepted Answer

The answer of The mean of a set of data...

Question 20

Provide an appropriate response.
-Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if it is at least three standard deviations above or
Below the mean. Round to the z-score to two decimal places, if necessary.
A department store, on average, has daily sales of $29,016.01. The standard deviation of sales is $
1500. On Tuesday, the store sold $35,503.73 worth of goods.

Accepted Answer

To find the z-score, use the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values: $z = \frac{(35503.73 - 29016.01)}{1500} = 4.33$. A z-score of 4.33 is more than three standard deviations away from the mean, making it unusual.

Quiz 3: Descriptive Measures

A variable x has a mean, µ, of 22 and a standard deviation, Ϭ, of 7. Determine the standardized version of x.

Find the median for the given sample data. -6, 7, 23, 21, 30, 46

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations. -Let $x _ { 1 } = 12 , x _ { 2 } = 17 , x _ { 3 } = 5 , x _ { 4 } = 1$ , and $x _ { 5 } = 7$ . Determine $\bar { x }$ .

Find the mode(s) for the given sample data. -The weights (in ounces) of 14 different apples are shown below. $\begin{array} { l l l l l l l } 5.4 & 4.3 & 4.6 & 5.8 & 4.0 & 5.4 & 4.3 \end{array}$ $\begin{array} { l l l l l l l } 5.3 & 5.6 & 5.8 & 5.4 & 5.3 & 5.8 & 6.3 \end{array}$

To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $\begin{array} { l l l l l l l l } \$ 410 & \$ 377 & \$ 395 & \$ 114 & \$ 293 & \$ 169 & \$ 140 & \$ 224 \end{array}$

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill has a roughly bell-shaped distribution with a mean of $57 and a standard deviation of $9. What percentage of her phone bills are between $30 and $84?

Obtain the five-number summary for the given data. 2, 3, 5, 8, 10

Find the range for the given data set. -Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores. 21 35 20 48 58

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Quiz 3: Descriptive Measures

A variable x has a mean, µ, of 22 and a standard deviation, Ϭ, of 7. Determine the standardized version of x.

Find the median for the given sample data. -6, 7, 23, 21, 30, 46

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations. -Let x1=12,x2=17,x3=5,x4=1x _ { 1 } = 12 , x _ { 2 } = 17 , x _ { 3 } = 5 , x _ { 4 } = 1x1​=12,x2​=17,x3​=5,x4​=1 , and x5=7x _ { 5 } = 7x5​=7 . Determine xˉ\bar { x }xˉ .

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill has a roughly bell-shaped distribution with a mean of $57 and a standard deviation of $9. What percentage of her phone bills are between $30 and $84?

Obtain the five-number summary for the given data. 2, 3, 5, 8, 10

Find the range for the given data set. -Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores. 21 35 20 48 58

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations. -Let $x _ { 1 } = 12 , x _ { 2 } = 17 , x _ { 3 } = 5 , x _ { 4 } = 1$ , and $x _ { 5 } = 7$ . Determine $\bar { x }$ .