Find the Value of a Normal Random Variable
-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 follows a normal distribution with an average of $600 per month and a standard deviation of $50 per month. Refer to such expenses as PCE s (personal call expenses). Find the point in the distribution below which 2.5% of the PCE s fell.
A) $502.00
B) $698.00
C) $15.00
D) $585.00

Question

Quizplus · Accepted Answer

To find the point below which 2.5% of the PCEs fell, we use the Z-score formula for a normal distribution, which is Z = (X - μ) / σ, where X is the value we seek, μ is the mean, and σ is the standard deviation. For the 2.5% lower tail of a normal distribution, the Z-score is approximately -1.96. Plugging in the values: -1.96 = (X - 600) / 50, solving for X gives us approximately $502.