Question 1

A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of 6 cartons.
a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61?
b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean?
c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

Accepted Answer

The answer of A supermarket has determined that daily demand...

Question 2

The mean of a sample of 15 measurements is 35.6. Suppose that the sample is enlarged to 16 measurements, by including one additional measurement having a value of 42. Find the mean of the sample of 16 measurements.

Accepted Answer

The answer of The mean of a sample of 15...

Question 3

How is the value of the correlation coefficient r affected in each of the following cases?
a. Each x value is multiplied by 4.
b. Each x value is switched with the corresponding y value.
c. Each x value is increased by 2.

Accepted Answer

The answer of How is the value of the correlation...

Question 4

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the lower quartile.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 5

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the upper quartile.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 6

a. Calculate the covariance and the coefficient of correlation for the following sample. $$\begin{array} { | l | r | r | r | r | r | } 
\hline x & 9 & 6 & 7 & 5 & 8 \
\hline y & 19 & 14 & 16 & 12 & 15 \
\hline
\end{array}$$ b. What do these statistics tell you about the relationship between X and Y?

Accepted Answer

The answer of a. Calculate the covariance and the coefficient...

Question 7

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the coefficient of variation.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 8

The following data are the heights (in cm) of the 25 students in a business statistics class: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 164 & 148 & 137 & 157 & 173 & 156 & 177 & 172 & 169 & 165 \
\hline 145 & 168 & 163 & 162 & 174 & 152 & 156 & 168 & 154 & 151 \
\hline 174 & 146 & 134 & 140 & 171 & & & & & \
\hline
\end{array}$$ Find the median height.

Accepted Answer

The answer of The following data are the heights (in...

Question 9

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the median salary.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 10

A sample of eight observations of variables x and y is shown below: $$\begin{array} { | l | r | r | r | r | r | r | r | r | } 
\hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \
\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \
\hline
\end{array}$$ Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

Accepted Answer

The answer of A sample of eight observations of variables...

Question 11

The following data are the heights (in cm) of the 25 students in a business statistics class: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 164 & 148 & 137 & 157 & 173 & 156 & 177 & 172 & 169 & 165 \
\hline 145 & 168 & 163 & 162 & 174 & 152 & 156 & 168 & 154 & 151 \
\hline 174 & 146 & 134 & 140 & 171 & & & & & \
\hline
\end{array}$$ a. Compute the sample mean height.
b. Compute the sample variance.
c. Compute the sample standard deviation.

Accepted Answer

The answer of The following data are the heights (in...

Question 12

A sample of eight observations of variables x and y is shown below: $$\begin{array} { | l | r | r | r | r | r | r | r | r | } 
\hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \
\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \
\hline
\end{array}$$ Draw the scatter diagram and plot the least-squares line.

Accepted Answer

The answer of A sample of eight observations of variables...

Question 13

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the mean salary.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 14

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the variance and standard deviation of the salaries.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 15

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the 90th percentile.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 16

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Compute the range.

Accepted Answer

The answer of The following data represent the salaries (in...

Question 17

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a mound-shaped distribution, what can we say about the proportion of ratios that fall between:
a. 11.5 and 15.5?
b. 9.5 and 17.5?
c. 7.5 and 19.5?

Accepted Answer

The answer of The price-earnings ratios of a sample of...

Question 18

A sample of 12 measurements has a mean of 25 and a standard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 25.
a. Find the mean of the sample of 14 measurements.
b. Find the standard deviation of the sample of 14 measurements.

Accepted Answer

The answer of A sample of 12 measurements has a...

Question 19

Given the following sample data: $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline x & 420 & 610 & 625 & 500 & 400 & 450 & 550 & 650 & 480 & 565 \
\hline y & 2.80 & 3.60 & 3.75 & 3.00 & 2.50 & 2.70 & 3.50 & 3.90 & 2.95 & 3.30 \
\hline
\end{array}$$ a. calculate the covariance and the correlation coefficient.
b. comment on the relationship between X and Y.
c. determine the least-squares line.
d. draw the scatter diagram and plot the least-squares line.

Accepted Answer

The answer of Given the following sample data: \[\begin{array} {...

Question 20

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$ Consider the following population of measurements: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 162 & 152 & 177 & 157 & 184 & 176 & 165 & 181 & 170 & 163 \
\hline
\end{array}$$ a. Compute the mean.
b. Compute the median.
c. Compute the variance and the standard deviation.

Accepted Answer

The answer of The following data represent the salaries (in...

Quiz 5: Numerical Descriptive Measures

The mean of a sample of 15 measurements is 35.6. Suppose that the sample is enlarged to 16 measurements, by including one additional measurement having a value of 42. Find the mean of the sample of 16 measurements.

How is the value of the correlation coefficient r affected in each of the following cases? a. Each x value is multiplied by 4. b. Each x value is switched with the corresponding y value. c. Each x value is increased by 2.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the lower quartile.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the upper quartile.

a. Calculate the covariance and the coefficient of correlation for the following sample. $\begin{array} { | l | r | r | r | r | r | } \hline x & 9 & 6 & 7 & 5 & 8 \\\hline y & 19 & 14 & 16 & 12 & 15 \\\hline\end{array}$ b. What do these statistics tell you about the relationship between X and Y?

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the median salary.

A sample of eight observations of variables x and y is shown below: $\begin{array} { | l | r | r | r | r | r | r | r | r | } \hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \\\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \\\hline\end{array}$ Draw the scatter diagram and plot the least-squares line.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the mean salary.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the 90th percentile.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array}{|l|l|l|l|l|l|l|}\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the range.

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a mound-shaped distribution, what can we say about the proportion of ratios that fall between: a. 11.5 and 15.5? b. 9.5 and 17.5? c. 7.5 and 19.5?