Julio observed that customer satisfaction ratings are normally distributed. If the 33rd percentile is 6.775, and the 65th percentile is 7.394 on a scale from 0-10 find the mean and standard deviation

Answer 1

Use the normalized value for the rating:

z = (x - mean)/SD, were x is the range, mean is the mean rating, SD is the standard deviation of the rating and z is the normalized value.

For the 33rd percentile, the z score is -0.44 and the rating is 6.775. plugging those values into the z equation above:

-0.44 = (6.775 - mean)/SD

-0.44*SD = 6.775 - mean

mean - 0.44*SD = 6.7775

For the 65th percentile, the z-score is 0.385 and the rating is 7.394. plugging those values into the z equation above:

0.385 = (7.394 - mean)/SD

0.385 * SD = 7.394 - mean

mean + 0.385 * SD = 7.394

We now have two equations in two unknowns and can solve for mean and SD.