Find and Interpret the Area under a Normal Curve
-A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution with an average of $800 per month and a standard deviation of $50 per month. Refer to such expenses as PCE s (personal call expenses). Using the distribution above, what is the probability that a randomly selected month had a PCE of between $675.00 and $890.00
A) 0.9579
B) 0.0421
C) 0.9999
D) 0.0001

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected month had a PCE between $675 and $890, we need to calculate the z-scores for these values and then find the area under the normal distribution curve between these z-scores. The z-score is calculated as $z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $675, $z = \frac{675 - 800}{50} = -2.5$, and for $890, $z = \frac{890 - 800}{50} = 1.8$. Looking these z-scores up in a standard normal distribution table or using a calculator, the area between these z-scores (which represents the probability) is approximately 0.9579.

Find and Interpret the Area Under a Normal Curve