Find the indicated probability.
-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.

Question

Quizplus · Accepted Answer

We need to find the probability of getting a rating between 170 and 220, which is equivalent to finding the area under the normal distribution curve between 170 and 220. We can standardize the values using the formula z = (x - μ) / σ, where x is the rating, μ is the mean, and σ is the standard deviation.

For 170, z = (170 - 200) / 50 = -0.6
For 220, z = (220 - 200) / 50 = 0.4

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:
P(z < -0.6) = 0.2743
P(z < 0.4) = 0.6554

The probability of getting a rating between 170 and 220 is the difference between these two probabilities:
P(170 < x < 220) = P(-0.6 < z < 0.4) = 0.6554 - 0.2743 = 0.3811

Therefore, the answer is C, 0.3811.

Find the Indicated Probability