Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per
Month. Refer to such expenses as PCEʹs (personal call expenses). Find the point in the distribution
Below which 2.5% of the PCEʹs fell.
A)$802.00
B)$22.50
C)$877.50
D)$998.00

Question

Quizplus · Accepted Answer

To find the point below which 2.5% of the PCE's fell, we use the Z-score formula for a normal distribution, which is Z = (X - μ) / σ, where X is the value in the distribution, μ is the mean, and σ is the standard deviation. For the 2.5% lower tail, the Z-score is approximately -1.96 (from standard normal distribution tables). Plugging in the values: -1.96 = (X - 900) / 50, solving for X gives X ≈ $802. This is the point below which 2.5% of the PCE's fell.

Before a New Phone System Was Installed, the Amount a Company