Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $500 per month and a standard deviation of $50 per
Month. Refer to such expenses as PCEʹs (personal call expenses). Using the distribution above,
What is the probability that during a randomly selected month PCEʹs were between $375.00 and
$590.00?
A).0421
B).0001
C).9999
D).9579

Question

Quizplus · Accepted Answer

To find the probability that the PCE's were between $375 and $590, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For $375: Z = (375 - 500) / 50 = -2.5. For $590: Z = (590 - 500) / 50 = 1.8. Looking these Z-scores up in a standard normal distribution table gives the probabilities of being below each value. The difference between these probabilities gives the probability of being between $375 and $590. This calculation results in a high probability, which matches option D, 0.9579, indicating that there's a 95.79% chance the PCE's were within this range.

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