Fill in the blanks by standardizing the normally distributed variable.
-The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 15 minutes and a standard deviation of 2 minutes. The percentage of
Time that the waiting time is less than 11 minutes is equal to the area under the standard normal
Curve that lies to the ___ of ___.
A)right, 0.6
B)right, -2
C)left, -2
D)left, 2

Question

Fill in the blanks by standardizing the normally distributed variable.
-The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 15 minutes and a standard deviation of 2 minutes. The percentage of
Time that the waiting time is less than 11 minutes is equal to the area under the standard normal
Curve that lies to the ___ of ___. 
A)right, 0.6
B)right, -2
C)left, -2
D)left, 2

Quizplus · Accepted Answer

To standardize the variable, we use the formula $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (11 minutes), $\mu$ is the mean (15 minutes), and $\sigma$ is the standard deviation (2 minutes). Substituting these values gives $Z = \frac{11 - 15}{2} = -2$. The percentage of time that the waiting time is less than 11 minutes corresponds to the area under the standard normal curve to the left of $Z = -2$.

Fill in the Blanks by Standardizing the Normally Distributed Variable