Question

Combined test scores were normally distributed with mean 1493 and standard deviation 342. Find the combined scores that correspond to these percentiles.
​a) 20th percentile
​b) 75th percentile
​c) 80th percentile

a) The combined scores that correspond to 20th percentile is about ___? ​(Round to the nearest integer as​ needed.)

​b) The combined scores that correspond to 75th percentile is about ___? ​(Round to the nearest integer as​ needed.)

​c) The combined scores that correspond to 80th percentile is about ___?​(Round to the nearest integer as​ needed.)

Answer 1

The combined scores that correspond to 20th percentile is about 1206.

The combined scores that correspond to 75th percentile is about 1724.

The combined scores that correspond to 80th percentile is about 1780.

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given the mean 1493 and standard deviation 342.

a) 20th percentile has a z score of -0.84, hence:

-0.84 = (x - 1493)/342

x = 1206

b) 75th percentile has a z score of 0.675, hence:

0.675 = (x - 1493)/342

x = 1724

c) 80th percentile has a z score of 0.84, hence:

0.84 = (x - 1493)/342

x = 1780

The combined scores that correspond to 20th percentile is about 1206.

The combined scores that correspond to 75th percentile is about 1724.

The combined scores that correspond to 80th percentile is about 1780.

Find out more on z score at: https://brainly.com/question/25638875