Question

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220. Your answer should be a decimal rounded to the fourth decimal place.

Answer 1

0.3811 is the probability that a randomly selected applicant will have a rating between 170 and 220.

Explanation:

We are given the following information in the question:

Mean, μ = 200

Standard Deviation, σ = 50

We are given that the distribution of ratings is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(rating is between 170 and 220)

`P(170 \leq x \leq 220)\\\\ = P(\displaystyle(170 - 200)/(50) \leq z \leq \displaystyle(220-200)/(50)) \\\\= P(-0.6 \leq z \leq 0.4)\\\\= P(z \leq 0.4) - P(z < -0.6)\\= 0.6554 - 0.2743 = 0.3811 = 38.11\%`

0.3811 is the probability that a randomly selected applicant will have a rating between 170 and 220.