# What is the minimum credit score needed by a 35-year-old applicant to be considered for a mortgage in the following case?The credit score of 35-year-olds applying for a mortgage at a particular...

What is the minimum credit score needed by a 35-year-old applicant to be considered for a mortgage in the following case?

The credit score of 35-year-olds applying for a mortgage at a particular institution is normally distributed with a mean of 600 and a standard deviation of 100. A private lender only wants to give a mortgage to applicants with credit scores in the top 6%.

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### 2 Answers

The credit score of 35-year-old applicants for a mortgage at a particular institution is normally distributed with a mean of 600 and a standard deviation of 100. The lender only wants to give a mortgage to applicants with credit scores in the top 6%.

To determine what the minimum credit score a 35 year old would need to be eligible for a mortgage use a normal distribution table to find the z-score that corresponds to a probability of 94%

This is equal to 1.56

The eligible credit score is Z, where (Z - 600)/100 = 1.56

=> Z - 600 = 156

=> Z = 756

**A 35 year old would need a minimum credit score of 756 to be eligible for a mortgage.**

Using a graphing utility or tables we find that the `z` score with 94% of the population beneath it is approximately 1.5548

Use `z=(x-mu)/sigma` to compute the required score.

`1.5548=(x-600)/100`

`x-600=155.48`

`x=755.48~~755.5`

So the lender will require a credit score `s>=755.5`