A study of Hub Furniture regarding the payment of invoices reveals the time from billing until payment is received follows the normal distribution. The mean time until payment is received is 20 days and the standard deviation is 5 days.


a. What percent of the invoices are paid within 15 days of receipt?

b. What percent of the invoices are paid in more than 28 days?

c. What percent of the invoices are paid in more than 15 days but less than 28 days?

d. The management of Hub Furniture wants to encourage their customers to pay their monthly invoices as soon as possible. Therefore, it announced that a 2 percent reduction in price would be in effect for customers who pay within 7 days of the receipt of the invoice. What percent of customers will earn this discount?

Z = (x - mean)/standard deviation

Find the respective Z scores forthe problems and look up the proportions cut off in a table in back of your stat book labeled something like "areas under the normal distribution." Convert these to percentages.

For example:

a. Z = (15 - 20)/5 = -5/5 = -1

On the table, that would be approximately 16%.

Use this method to do the other problems.

I hope this helps.

To answer these questions, we need to use the properties of the normal distribution and calculate the z-scores corresponding to the given values.

a. To find the percent of invoices paid within 15 days, we need to find the area under the curve to the left of 15 days.
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the value in question, μ is the mean, and σ is the standard deviation.
Therefore, z = (15 - 20) / 5 = -1.
Using a standard normal distribution table (or a calculator), we can find that the area to the left of -1 is approximately 0.1587.
So, about 15.87% of invoices are paid within 15 days of receipt.

b. To find the percent of invoices paid in more than 28 days, we need to find the area under the curve to the right of 28 days.
Calculating the z-score: z = (28 - 20) / 5 = 1.6.
Using the standard normal distribution table, the area to the right of 1.6 is approximately 0.0548.
So, about 5.48% of invoices are paid in more than 28 days.

c. To find the percent of invoices paid in more than 15 days but less than 28 days, we need to find the area under the curve between these two values.
First, we calculate the z-scores for both 15 and 28 days:
z1 = (15 - 20) / 5 = -1,
z2 = (28 - 20) / 5 = 1.6.
Using the standard normal distribution table again, we find the area to the left of -1 is approximately 0.1587 and to the right of 1.6 is approximately 0.0548.
To find the area between -1 and 1.6, we subtract the smaller area from the larger area: 0.0548 - 0.1587 = 0.1039.
So, about 10.39% of invoices are paid in more than 15 days but less than 28 days.

d. To find the percent of customers who will earn the discount for paying within 7 days, we need to find the area under the curve to the left of 7 days.
Calculating the z-score: z = (7 - 20) / 5 = -2.6.
Using the standard normal distribution table, we find the area to the left of -2.6 is approximately 0.0047.
So, about 0.47% of customers will earn the discount for paying within 7 days.