Question

In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 30 with a standard deviation of 7 days. Assume the data to be approximately bell-shaped.

Between what two values will approximately 68% of the numbers of days be?
Approximately 68% of the customer accounts have payment made between __________and________________ days

Answer 1

The answer is 16 and 44 days.

Explanation:

This is the correct answer for this question.

Answer 2

Approximately 68% of the customer accounts have payment made between 23 and 37 days.

Explanation:

We want to calculate what two values will approximately 68% of the numbers of days be.

For a bell shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.

Then, for a mean of 30 and standard deviation of 7, we can calculate the two values as:

`X_1=\mu+z_1\cdot\sigma=30-1\cdot 7=30-7=23 \\\\X_2=\mu+z_2\cdot\sigma=30+1\cdot 7=30+7=37`