CFA Level 1: Payment of Invoices and Distribution Analysis

Payment of Invoices

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Question

A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

Answers

Explanations

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A. B. C. D. E.

C

z = (x-u)/sigma = 15 - 20/5 = -1.0. z = 1 is 0.3413. 1.0 - 0.8413 = 0.1587.

To solve this question, we need to use the concept of z-scores, which is a measure of how many standard deviations an observation is from the mean in a normal distribution.

Given information: Mean (average) payment period = 20 days Standard deviation = 5 days

To find the percentage of invoices paid within 15 days of receipt, we need to determine the z-score for the value of 15 days and then look up the corresponding percentage in the standard normal distribution table.

The z-score formula is:

z = (X - μ) / σ

Where: X is the value we are interested in (15 days) μ is the mean (20 days) σ is the standard deviation (5 days)

Plugging in the values:

z = (15 - 20) / 5 z = -1

Now we need to find the percentage of invoices paid within -1 standard deviation from the mean in a standard normal distribution.

Looking up the z-score of -1 in the standard normal distribution table, we find that the corresponding percentage is approximately 0.1587 or 15.87%.

Therefore, the answer is option C: 15.87%.

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