Question
The manager at a new bank wants to hire enough tellers to ensure no customer waits in line too long. To gather more information, she waits in line at other local banks.
At each bank the manager notes the number of teller windows that are open, x, as well as the number of minutes she has to wait in line before being served, y.
The least squares regression line of this data set is:
y=
–
4.956x+32.186
If 3 windows are open, how much time does this line predict will be spent waiting in line?
Round your answer to the nearest thousandth.
minutes
At each bank the manager notes the number of teller windows that are open, x, as well as the number of minutes she has to wait in line before being served, y.
The least squares regression line of this data set is:
y=
–
4.956x+32.186
If 3 windows are open, how much time does this line predict will be spent waiting in line?
Round your answer to the nearest thousandth.
minutes
Answers
GPT-4o mini
To predict the waiting time when 3 teller windows are open, we can plug \( x = 3 \) into the regression equation:
\[
y = -4.956x + 32.186
\]
Substituting \( x = 3 \):
\[
y = -4.956(3) + 32.186
\]
Calculating \( -4.956(3) \):
\[
-4.956 \times 3 = -14.868
\]
Now, adding this result to 32.186:
\[
y = -14.868 + 32.186
\]
Calculating this:
\[
y = 17.318
\]
Therefore, when 3 windows are open, the predicted waiting time in line is approximately **17.318 minutes**.
\[
y = -4.956x + 32.186
\]
Substituting \( x = 3 \):
\[
y = -4.956(3) + 32.186
\]
Calculating \( -4.956(3) \):
\[
-4.956 \times 3 = -14.868
\]
Now, adding this result to 32.186:
\[
y = -14.868 + 32.186
\]
Calculating this:
\[
y = 17.318
\]
Therefore, when 3 windows are open, the predicted waiting time in line is approximately **17.318 minutes**.