In a large sample of customer accounts, Consumer\'s energy determined that the a

Question

In a large sample of customer accounts, Consumer's energy determined that the average number of days between when a bill was sent out and when the payment was made is 32 days with a variance of 49 days^2. Assume the data to be approximately bell-shaped. Compute the standard deviation of days for a bill to be paid Construct and label a bell-graph (with parameters and percentages labeled - pay close attention to spacing and scale Roughly 68% of all customer accounts are paid between what time frames? Estimate the percentage of customer accounts for which payment is made between 32 and 53 days. Estimate the percentage of customer accounts for which payment is made in 46 days or less. Would it be unusual for a customer to pay in less than 18 days? Explain.

Explanation / Answer

a )

Variance = 49

Standard deviation = ÖVariance = Ö49 = 7

Answer: 7

( b )

                                                                                                                                    

                                         11     18     25       32     39      46        53

( c )

Using empirical rule 68% will lie between mean and 1 standard deviation. So here the answers are 25 and 39.

Answer: 25 and 39

( d )

Using empirical rule we can say that between mean and 3 standard deviation the approximated area is 0.4985 (0.997/2).

Answer: 0.4985

( e )

Using empirical rule here the percentage is 0.9735 ((0.997/2) + (0.95/2) ).

Answer: 0.9735

( f )

Probability of less than 18 is = ((0.997/2) – (0.95/2) ) = 0.0235

Here this probability is less than .05 so we can say that for a customer to pay in less than 18 days is unusual.

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