Question

The credit scores of 32-year-old mortgage applicants at Directions Credit Union are normally distributed with a mean of 621 and a standard deviation of 102. Round your answers to four decimal places. (a) What is the probability that a randomly selected 32-year-old mortgage applicant has a credit score lower than 811?

Answer 1

0.96856

Explanation:

Given info:

μ = 621

σ = 102

Find: P(X < 811)

First, find the z-score:

z = (x - μ)/σ

z = (811 - 621)/102

z = 1.86

Since z = 1.86, this means x is 1.86 standard deviations from the mean. With this information, we can use a standard normal table to find the probability that a randomly selected 32-year-old mortgage applicant has a credit score lower than 811.

Using the standard normal table, we get a probability of 0.96856

Alternatively, we can get the same answer using software. Note: The answer is slightly different due to rounding.