The average credit score in Canada is 650. Assume that credit scores follow a normal distribution with a standard deviation of 80.(round each to the nearest integer)

Question

a) Find the 80th percentile of credit scores in Canada.

b) 75% of Canadians have a credit score higher than what value?

c) Mac’s credit score is 770. In what percentile is his credit score?

Answer 1

use z = (x - mean)/SD which is N(01) where x is credit score, mean = 650 and SD = 80

a) find z-score corresponding to 80th percentile (probability of 0.8). plug in value for z-score, mean and SD and solve for x.

b) find z-score corresponding to 75th percentile (probability of 0.75). plug in value for z-score, mean and SD and solve for x.

c) plug in x = 770, SD and mean, and get z-score. Look up probability corresponding to z-score and multiply by 100 to get percentile.