Question

The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, where the amount requested for home loans followed the normal distribution with a mean of $73000 and a standard deviation of $22000. (Round z-score computation to 2 decimal places and the final answers to the nearest whole dollars.)

a. What is the minimum amount requested on the largest 4% of loans?_______ $
b. What is the maximum amount requested on the smallest 14% of loans? _________$

Answer 1

The minimum amount on the largest 4% of home loan applications is approximately $111,500. The maximum amount on the smallest 14% of loans is approximately $50,240. These values are found using the standard normal distribution and the provided mean and standard deviation.

Step-by-step explanation:

The question involves finding specific values from a normal distribution of home loan amounts with parameters - a mean of $73,000 and a standard deviation of $22,000.

Part a

To find the minimum amount requested on the largest 4% of loans, we first need to find the z-score that corresponds to the top 4% of a standard normal distribution. We can use a z-table or a normal distribution calculator for this. The z-score that corresponds to the top 4% is approximately 1.75. We can then use the z-score formula to find the corresponding amount:

Z = (X - mean) / standard deviation

1.75 = (X - 73,000) / 22,000

X = (1.75 * 22,000) + 73,000

X ≈ $111,500

Part b

For the maximum amount on the smallest 14% of loans, we want the z-score at the 14th percentile, which is approximately -1.08. Using the z-score formula again:

-1.08 = (X - 73,000) / 22,000

X = (-1.08 * 22,000) + 73,000

X ≈ $50,240

The minimum amount on the largest 4% of home loan applications is approximately $111,500, and the maximum amount on the smallest 14% of home loans is approximately $50,240.