Answered: Refer to the Century National Bank…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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.

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

1. Microsoft Excel spreadsheet showing detailed descriptive analysis.

2. Microsoft Word file with executive summary of with written analysis for Mr. Selig. (250
words minimum)

### Bank Account Data Overview

This table presents data from 60 different bank accounts, covering various attributes related to the accounts. The columns are defined as follows:

- **$ x_1 $**: Account balance in $
- **$ x_2 $**: Number of ATM transactions in the month
- **$ x_3 $**: Number of other bank services used
- **$ x_4 $**: Has a debit card (1 = yes, 0 = no)
- **$ x_5 $**: Receives interest on the account (1 = yes, 0 = no)
- **$ x_6 $**: City where banking is done

Below is the detailed data for the 60 accounts:

| $ x_1 $ | $ x_2 $ | $ x_3 $ | $ x_4 $ | $ x_5 $ | $ x_6 $ |
|-----------|-----------|-----------|-----------|-----------|-----------|
| 1,756 | 13 | 4 | 0 | 1 | 2 |
| 748 | 9 | 2 | 1 | 0 | 1 |
| 1,501 | 10 | 1 | 0 | 1 | 0 |
| 1,831 | 10 | 0 | 1 | 1 | 1 |
| 1,622 | 14 | 6 | 0 | 1 | 4 |
| 1,886 | 17 | 3 | 0 | 1 | 1 |
| 740 | 6 | 3 | 0 | 1 | 3 |
| 1,593 | 10 | 8 | 1 | 0 | 1 |
| 1,169 | 6 | 4 | 0 | 1 | 3 |
| 2,125 | 18 | 8 | 0 | 1 | 4 |
| 1,554 | 12 | 6 | 1 | 0 | 1

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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