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?
A) 15.87%
B) 37.91%
C) 34.13%
D) 86.74%

Question

Quizplus · Accepted Answer

To solve the problem, we need to use the z-score formula:

z = (x - μ) / σ

Where:
x = 15 (the number of days we want to find the percentage for)
μ = 20 (the mean)
σ = 5 (the standard deviation)

Plugging in the values, we get:

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

Using the z-table or a calculator with a normal distribution function, we can find the area to the left of z = -1, which represents the percentage of invoices paid within 15 days. The result is 0.1587, or 15.87% rounded to two decimal places. Therefore, the best choice is A) 15.87%.

A Study of a Company's Practice Regarding the Payment of Invoices