Question

In a recent study on world happiness, participants were asked were to evaluate their current lives on a scale from 0-10,where o represents the worst possible life and 10 represents the best possible life. Then mean response was 5.4 with a standard deviation of 2.3

A. what response represents the 86TH Percentile?
B. what response represents the 56 Percentile?
c.what response represents the first quartile?​

Answer 1

Explanation:

Let's assume that we can apply the central limit thereom

the z score that associates with .86 is about 1.08

so

1.08=(x-5.4)/2.3

x= 7.884

The zscore that associates with .56 is .15

.15=(x-5.4)/2.3

x=5.745

The first quartile is equal to the 25th percentile

the 25th percentile has a z score is closest to -.67

-.67=(x-5.4)/2.3

x=3.859