A store owner recorded the total number of customers that visited his store at the end of each hour that the store was open. He created the scatterplot, trend line, and equation below based on the data.

Question

Store Customers
A graph has hours open on the x-axis, and total customers on the y-axis. A trend line has a regression equation of y = 25.36 x minus 0.23.

Assuming that the trend continues, which is the best estimate for the number of hours that the store will have been open when the total customer count is 310?
11
12
13
14

Answer 1

To find the number of hours when the total customer count is 310, we can use the given regression equation:

\[ y = 25.36x - 0.23 \]

where \( y \) is the total number of customers and \( x \) is the number of hours the store has been open.

We need to find \( x \) when \( y = 310 \):

\[ 310 = 25.36x - 0.23 \]

Now, let's solve for \( x \):

1. Add 0.23 to both sides:

\[ 310 + 0.23 = 25.36x \]

\[ 310.23 = 25.36x \]

2. Divide both sides by 25.36:

\[ x = \frac{310.23}{25.36} \]

Calculating this:

\[ x \approx 12.23 \]

Since we need to find the best estimate, we look at the options provided: 11, 12, 13, and 14. The best estimate for the number of hours the store will have been open when the total customer count is 310 is:

12 hours.