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 14 minutes and a standard deviation of 3 minutes. The percentage of
Time that the waiting time exceeds 12 minutes is equal to the area under the standard normal curve
That lies to the ___ of ___.
A)left, -0.67
B)right, -0.67
C)left, 0.64
D)right, 0.67

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 14 minutes and a standard deviation of 3 minutes. The percentage of
Time that the waiting time exceeds 12 minutes is equal to the area under the standard normal curve
That lies to the ___ of ___. 
A)left, -0.67
B)right, -0.67
C)left, 0.64
D)right, 0.67

Quizplus · Accepted Answer

To find the standardized score (z-score) for 12 minutes, use the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is 12 minutes, $\mu$ is 14 minutes (mean), and $\sigma$ is 3 minutes (standard deviation). This gives $z = \frac{12 - 14}{3} = -\frac{2}{3} = -0.67$. The percentage of time that the waiting time exceeds 12 minutes corresponds to the area under the curve to the right of $z = -0.67$.

Fill in the Blanks by Standardizing the Normally Distributed Variable