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Complete the following CNP Bank Card Case and answer the accompanying questions.

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Before banks issue a credit card, they usually rate or score the customer in terms of their projected probability of being a profitable customer. A typical scoring table appears below.

**Age**
- Under 25: 12 pts.
- 25–29: 5 pts.
- 30–34: 0 pts.
- 35+: 18 pts.

**Time at Same Address**
- < 1 yr.: 9 pts.
- 1–2 yrs.: 0 pts.
- 3–4 yrs.: 13 pts.
- 5+ yrs.: 20 pts.

**Auto Age**
- None: 18 pts.
- 0–1 yr.: 12 pts.
- 2–4 yrs.: 13 pts.
- 5+ yrs.: 3 pts.

**Monthly Car Payment**
- None: 15 pts.
- $1–$99: 6 pts.
- $100–$299: 4 pts.
- $300+: 0 pts.

**Housing Cost**
- $1–$199: 0 pts.
- $200–$399: 10 pts.
- Owns: 12 pts.
- Lives with relatives: 24 pts.

**Checking/Savings Accounts**
- Both: 15 pts.
- Checking Only: 3 pts.
- Savings Only: 2 pts.
- Neither: 0 pts.

The score is the sum of the points on the six items. For example, Sushi Brown is under 25 years old (12 pts.), has lived at the same address for 2 years (0 pts.), owns a 4-year-old car (13 pts.), with car payments of $75 (6 pts.), housing cost of $200 (10 pts.), and a checking account (3 pts.). She would score 44. A second chart is then used to convert scores into the probability of being a profitable customer. A sample chart of this type appears below.

| Score | 30 | 40 | 50 | 60 | 70 | 80 | 90 |
|--------|----|----|----|----|----|----|----|
| Probability | .70 | .78 | .85 | .90 | .94 | .95 | .96 |

Sushi’s score of 44 would translate into a probability of being profitable of approximately .81. In other words, 81 percent of customers like Sushi will make money for the bank card operations.

Here are the interview results for three potential customers:

| Name | David | Edward | Ann |
|------|-------|--------|-----|
| Age | 42 | 23 | 33 |
| Time at same address | 9 | 2 | 5 |
| Auto age | 2 | 3 | 7 |
| Monthly car payment | $140 | $99 | $175 |
| Housing cost | $300 | $200 | Owns clear |
| Checking/savings accounts | Both | Checking only | Neither |

Score each of these customers and estimate their probability of being profitable.

1. What is the probability that all three are profitable?
2. What is the probability that none of them are profitable?
3. Find the entire probability distribution for the number of profitable customers among this group of three.

Write a brief summary of your findings.

Answer :

The probability that all three are profitable is 66.15% and the probability that none of them are profitable is 0.11%.

The probability distribution for the number of profitable customers is

X 0 1 2 3

P(X) 0.0011 0.1421 0.3065 0.5503

Name Born Age Time at same address Auto age Monthly car payment Housing cost Checking/savings accounts Score
David 42 9 2 $140 $300 Both 52
Edward 23 2 3 $99 $200 Checking only 23
Ann 33 5 7 $175 Owns clear Neither 69

We have to fill up the following table after scoring all the potential customers.

Name Born Age Time at same address Auto age Monthly car payment Housing cost Checking/savings accounts Score
David 42 18 20 4 0 15 52
Edward 23 0 9 13 6 10 23
Ann 33 18 0 3 4 2 69

To calculate the probability of each customer being profitable, we need to refer to the chart below:

Score 30 40 50 60 70 80 90

Probability .70 .78 .85 .90 .94 .95 .96

David’s score is 52 which corresponds to a probability of .90. Edward’s score is 23 which corresponds to a probability of .78. Ann’s score is 69 which corresponds to a probability of .95.

The probability that all three are profitable is equal to the product of the probability that each customer is profitable:
0.9 * 0.78 * 0.95 = 0.66147 or about 66.15%

The probability that none of them are profitable is equal to the product of the probability that each customer is not profitable:

0.1 * 0.22 * 0.05 = 0.0011 or about 0.11%

Find the entire probability distribution for the number of profitable customers among this group of three.

Let’s define the random variable X as the number of profitable customers among the three. The possible values for X are 0, 1, 2, or 3. The probabilities are as follows:

X 0 1 2 3

P(X) 0.0011 0.1421 0.3065 0.5503

In conclusion, the bank should approve the credit card application of Ann since there is a 95% chance that she will be a profitable customer. David has a 90% chance of being profitable so the bank can approve his credit card application too. However, Edward has only a 78% chance of being profitable so the bank should probably decline his credit card application. The probability that all three customers are profitable is 66.15% while the probability that none of them are profitable is 0.11%. The probability distribution of the number of profitable customers among the three is shown above.

Learn more about Probability:

https://brainly.com/question/25839839

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