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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 31 with a standard deviation of 3 days. Assume the data to be approximately bell-shaped. Approximately 37% of all customer accounts have the average number of days between two values A and B. What is the value of B?

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Answer:

B = 32.44 = 32 days

Explanation:

Given the following :

Mean number of days between when Bill was sent out and when payment was made = 31

Standard deviation = 3 days

Approximately 37% of all customer accounts have the average number of days between two values A and B. What is the value of B?

Interval A and B contains 37% of all customer accounts have average number of days with values :

Zscore of the (100-37)% / 2 at the extremes ; = 63%/2 = 0.315 ; from z table 0.315 = -0.48

Interval:

(-0.48 * sd) + mean and (0.48 * sd) + mean

(-0.48 * 3) + 31 and (0.48 * 3) + 31

-1. 44 + 31 and 1.44 + 31

29.56 and 32.44

Value of A and B

A = 29.56 ; B = 32.44

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