Assignment:
NOTE: The difference between the theoretical normal distribution and the actual, or observed, distribution is the same for any "theoretical vs actual. A theoretical distribution describes expected values of a variable in an entire population in the long run over successive events or experiments. An actual, or empirical, distribution would be based on observed values, for example converting a run of observations to z-scores gives the distribution of a variable, either for a sample, or for an observable population.
Estimate what the theoretical distribution would predict for the bank balances and compare this to the observed values. I am asked to used z-scores to determine probabilities that a value will be, e.g. below $500, then count the observed values below $500 and compare the counted, or actual number of observed values to what would be predicted using the normal distribution.
a. Is it reasonable that the distribution of checking account balances approximates a normal distribution?
b. Determine the mean and the standard deviation for the sample of 60 customers.
c. Compare the actual distribution with the theoretical distribution.
d. Cite some specific examples and comment on your findings.
e. 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.
f. 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?
g. Cite some examples and comment on your findings.
Checking Account Balances (60 accounts)
1616 1756
748 1501
1831 1622
1886 740
1593 1169
2125 1554
1474 1913
1218 1006
2215 137
167 343
2557 2276
1494 2144
1995 1053
1526 1120
1838 1746
1958 634
580 1320
1675 789
1735 1784
1326 2051
1044 1885
1790 765
1645 32
1266 890
2204 2409
1338 2076
1708 2138
2375 1455
1487 1125
1989 2156
60 checking accounts broken down into four different branches
Ohio Georgia Kentucky Pensylvania
343 1125 32 167
580 1338 137 634
748 1526 740 765
890 1616 1053 789
1006 1675 1120 1169
1044 1746 1326 1266
1218 1756 1455 1487
1320 1885 1554 1622
1474 1958 1735 1645
1494 1989 1790 2051
1501 1995 1831 2138
1593 2076 1838 2215
1708 2125 2144 2557
1784 2156 2276
1886 2204
1913 2375
2409