Question

Expenses for personal calls at a company are normally distributed and cost on average $399.50 per month with standard deviation $49.75. Find the amount below which 33% of the expenses fall.

Answer 1

To find the amount below which 33% of the monthly expenses for personal calls at a company fall, one must calculate the Z-score for the 33rd percentile and then apply the formula incorporating the mean and standard deviation. The result is $377.61.

Step-by-step explanation:

The student is asking to find the amount below which 33% of the expenses for personal calls at a company fall, knowing that the expenses are normally distributed and have an average cost of $399.50 per month with a standard deviation of $49.75. To answer this, we can use the concept of Z-scores and the normal distribution.

First, we need to find the Z-score that corresponds to the 33rd percentile of a normal distribution. This can be done using a standard normal distribution table or a calculator with statistical functions.

Once we have the Z-score, we calculate the value using the formula:
Value = Mean + (Z-score * Standard Deviation)

Assuming a Z-score for the 33rd percentile is approximately -0.44 (this value can vary slightly depending on the source), we can calculate:

Value = $399.50 + (-0.44 * $49.75) = $399.50 - $21.89 = $377.61

Therefore, 33% of the expenses fall below $377.61.