Question

Suppose that the loan amount on mortgages for a particular zip code is normally distributed with a mean of 154,449, measured in dollars, with a standard deviation of 14,794. What is the z value for a loan of 162,443 dollars? Answer to three decimal places if needed.

Answer 1

Answer:

The z value for a loan of 162,443 dollars is 0.5404.

Step-by-step explanation:

We are given that the loan amount on mortgages for a particular zip code is normally distributed with a mean of 154,449, measured in dollars, with a standard deviation of 14,794.

Let X = loan amount on mortgages for a particular zip code

So, X ~ N($\mu=154,449,\sigma^{2}=14,794^{2}$)

Now, the z score probability distribution is given by;

          Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean loan amount = $154,449

            $\sigma$ = standard deviation = $14,794

So, the z-score for a loan of 162,443 dollars is given by;

               Z = $\frac{162,443 - 154,449}{14,794}$

                  = $\frac{7,994}{14,794}$ = 0.5404

Therefore, the z value for a loan of 162,443 dollars is 0.5404.