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# Century National Bank

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Century National Bank

Refer to the Century National Bank data (attached).

Is it reasonable that the distribution of checking account balances approximates a normal probability distribution? Determine the mean and the standard deviation for the sample of 60 customers. Compare the actual distribution with the theoretical distribution. Cite some specific examples and comment on your findings.

Divide the account balances into three groups, of about 20 each, with the smallest third of the balances in the first group, the middle third in the second group, and those with the largest balances in the third group. Next, develop a table that shows the number in each of the categories of the account balances by branch. Does it appear that account balances are related to the branch? Cite some examples and prepare a short written report of your findings in Microsoft Word.

https://brainmass.com/statistics/hypothesis-testing/century-national-bank-528778

#### Solution Preview

1) To find out the mean and standard deviation for the variable x1, we could run "descriptive statistics" under "data analysis" in excel. Based on the output on the left, we could see that mean is 1499.867, standard deviation is 596.9049. For the normal distribution, median should be equal or very close to mean. However, for this data set, the median is 1604.5, quite different from mean of 1499.867. Therefore, this data set does not follow ...

#### Solution Summary

The expert examines Century National Bank distribution accounts.

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## Century National Bank Scatter Diagram and Correlations

1) Compute/answer the following about the variables "Balance" and "ATM", fr om the Century National Bank Data Set.

a) Develop a scatter diagram that represents the question, do higher balances lead to higher usage of ATMs?
b) The coefficient of correlation (interpret)
c) The coefficient of determination (interpret)
d) Is the coefficient of correlation significant at the .05 level of significance (conduct a hypothesis test for this)?
e) The regression equation that answers the question, do higher balances lead to higher usage of ATMs?
f) How many times would you predict the ATM would be used by someone with a balance of \$650?

Balance ATM Services Debit Interest City
1756 13 4 0 1 2
748 9 2 1 0 1
1501 10 1 0 0 1
1831 10 4 0 1 3
1622 14 6 0 1 4
1886 17 3 0 1 1
740 6 3 0 0 3
1593 10 8 1 0 1
1169 6 4 0 0 4
2125 18 6 0 0 2
1554 12 6 1 0 3
1474 12 7 1 0 1
1913 6 5 0 0 1
1218 10 3 1 0 1
1006 12 4 0 0 1
2215 20 3 1 0 4
137 7 2 0 0 3
167 5 4 0 0 4
343 7 2 0 0 1
2557 20 7 1 0 4
2276 15 4 1 0 3
1494 11 2 0 1 1
2144 17 3 0 0 3
1995 10 7 0 0 2
1053 8 4 1 0 3
1526 8 4 0 1 2
1120 8 6 1 0 3
1838 7 5 1 1 3
1746 11 2 0 0 2
1616 10 4 1 1 2
1958 6 2 1 0 2
634 2 7 1 0 4
580 4 1 0 0 1
1320 4 5 1 0 1
1675 6 7 1 0 2
789 8 4 0 0 4
1735 12 7 0 1 3
1784 11 5 0 0 1
1326 16 8 0 0 3
2051 14 4 1 0 4
1044 7 5 1 0 1
1885 10 6 1 1 2
1790 11 4 0 1 3
765 4 3 0 0 4
1645 6 9 0 1 4
32 2 0 0 0 3
1266 11 7 0 0 4
890 7 1 0 1 1
2204 14 5 0 0 2
2409 16 8 0 0 2
1338 14 4 1 0 2
2076 12 5 1 0 2
1708 13 3 1 0 1
2138 18 5 0 1 4
2375 12 4 0 0 2
1455 9 5 1 1 3
1487 8 4 1 0 4
1125 6 4 1 0 2
1989 12 3 0 1 2
2156 14 5 1 0 2

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