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 34 with a standard deviation of 9 days. Assume the data to be approximately bell-shaped. You can use the side spaces to sketch the distribution.

a) Between what two values will approximately 68% of the numbers of days be?

b) Approximately what percentage of customer accounts will have the number of days between 16 and 52 days?

c) What percent of customer accounts have the number of days less than 43 days?

d) What does it mean for a customer to have a z-score of -1.8, in terms of when they pay their bills?

Answer 1

Approximately 68% of payments are made between 25 to 43 days; around 95% of payments are made between 16 to 52 days; approximately 68% of payments are made in less than 43 days; a z-score of -1.8 indicates payment much earlier than average.

Step-by-step explanation:

The student is asking about the application of the empirical rule to a distribution of customer payment times for a utility company. Specifically, the questions seek to apply the rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and about 99.7% within three standard deviations.

a) Approximately 68% of the number of days will be between 25 days (mean - 1 SD) and 43 days (mean + 1 SD).

b) Between 16 and 52 days, which represents mean ± 2 SDs, approximately 95% of the customer accounts will have the number of days.

c) Less than 43 days, which is within 1 SD of the mean, approximately 68% of the customer accounts have the number of days.

d) A customer with a z-score of -1.8 means they pay their bills significantly earlier than the average, around 1.8 standard deviations before the mean of 34 days.