Questions: Data table Number of sales people working Sales (in 1000) ------ 3 11 4 12 6 14 9 15 11 19 11 21 12 21 15 23 17 23 18 25 x=10.6 y=18.4 SD(x)=5.19 SD(y)=5.02 Data from a small bookstore are shown in the accompanying table. The correlation for the data is 0.972. Complete parts a through d. a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales to be? Sales should be standard deviation(s) the mean. (Round to two decimal places as needed.)

Data table

Number of sales people working Sales (in 1000)
------
3 11
4 12
6 14
9 15
11 19
11 21
12 21
15 23
17 23
18 25
x=10.6 y=18.4
SD(x)=5.19 SD(y)=5.02

Data from a small bookstore are shown in the accompanying table. The correlation for the data is 0.972. Complete parts a through d.

a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales to be?

Sales should be standard deviation(s) the mean. (Round to two decimal places as needed.)

Transcript text: Data table \begin{tabular}{c|c} \hline \begin{tabular}{c} Number of sales \\ people working \end{tabular} & Sales (in $\$ 1000$ ) \\ \hline 3 & 11 \\ 4 & 12 \\ 6 & 14 \\ 9 & 15 \\ 11 & 19 \\ 11 & 21 \\ 12 & 21 \\ 15 & 23 \\ 17 & 23 \\ 18 & 25 \\ $x=10.6$ & $y=18.4$ \\ $S D(x)=5.19$ & $S D(y)=5.02$ \\ \hline \end{tabular} Data from a small bookstore are shown in the accompanying table. The correlation for the data is 0.972 . Complete parts a through d. a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales to be? Sales should be $\square$ standard deviation(s) $\square$ the mean. (Round to two decimal places as needed.)

Solution

Solution Steps

To solve this problem, we use the concept of correlation and standard deviation. Given the correlation coefficient, we can determine how many standard deviations sales are expected to be from the mean when the number of salespeople is a certain number of standard deviations from its mean. Specifically, we multiply the correlation coefficient by the number of standard deviations the number of salespeople is from the mean.

Step 1: Understand the Problem

We need to determine how many standard deviations sales are expected to be from the mean when the number of salespeople is 2 standard deviations above the mean, given a correlation coefficient of 0.972.

Step 2: Apply the Correlation Concept

The relationship between the number of salespeople and sales is given by the correlation coefficient. If the number of salespeople is $2$ standard deviations above the mean, the expected number of standard deviations for sales is calculated as: \[ \text{Expected Standard Deviations for Sales} = \text{Correlation} \times \text{Standard Deviations for Salespeople} \] Substituting the given values: \[ = 0.972 \times 2 \]

Step 3: Calculate the Expected Standard Deviations

Perform the multiplication: \[ = 1.944 \]