Question

1. Refer to the Century National Bank data. 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.

2. 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 comment on your findings

this has already been posted on your site but the work how you got these answers are not please help!!

Answer 1

1.Number of customers, n = 60

Actual distribution:

Balance                         |                                  Freq                 |                            Relative Freq|

0 up to 421                   |                                     4                     |                                     0.0667 |

422 up to 843                |                                     6                     |                                          0. 1|

844 up to 1264              |                                    8                     |                                     0. 1333|

1265 up to 1685            |                                  16                     |                                     0. 2667|

1686 up to2106             |                                    16                    |                                    0. 2667|

2107 up to 2527            |                                     9                    |                                         0. 15|

528 up to 2948              |                                    1                     |                                    0. 0167|

Total                             |                                   60                     |                                              1|

The following table above was extracted from the sample set of data. it can be seen that the

distribution of the checking account balances approximates a normal probability distribution.

Comparison of actual distribution with theoretical distribution:- * Actual distribution: Class ($1686 up to $2106) = 0. 2667 (relative frequency) * Theoretical distribution:

Using Z formula:- For X = 1686For X = 2106 P (between $1686 and $2106) = 0. 3531 – 0. 1255 = 0. 2276 From the example taken (between $1686 and $2106), it can be seen that there is some difference in the probability calculated.

Actual distribution yields the probability value of 0. 2667 whereby theoretical distribution yields the value 0. 2276. Margin of error is to be expected considering the large sample size. The probability of the sample size is to give a rough estimate on the actual values.

2.

From this table, it indicates that the categories of account balances (smallest, middle and largest

balance) are related to the branch. This is because smallest amount of account balances was mostly deposited in Branch 1 (Cincinnati, Ohio) and largest amount of account balances was mostly deposited in Branch 2 (Atlanta, Georgia). CONCLUSION 1. Based on the sample data, at 95% confidence level, it can be concluded that more than 50% of the customers use the debit card. 2.The mean checking balance for Century National Bank is concluded to be similar or more than $1600 which is almost same for many years. 3. The mean number of transactions per month per customer is concluded to be greater than 9. Therefore, the advertising agency can say the mean is more than 9 per month. But, there is no sufficient evidence to conclude that the mean is more than 10 per month. 4. There is some difference in the probability calculated. Actual distribution yields the probability value of 0. 2667 whereby theoretical distribution yields the value 0. 2276. Margin of error is to be expected considering the large sample size. 5. It can be concluded that the categories of account balances (smallest, middle and largest balance) are related to the branch.