Question

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.8 with a standard deviation of 2.3.

​(a) What response represents the 91st ​percentile? ​

(b) What response represents the 65th ​percentile?

​(c) What response represents the first ​quartile?

Answer 1

Given that,

mean = = 5.8

standard deviation = = 2.3

Using standard normal table,

P(Z < z) = 91%

= P(Z < z) = 0.91

= P(Z <1.34 ) = 0.91

z = 1.34

Using z-score formula  

x= z * +

x= 1.34*2.3+5.8

x= 8.882

x=9

(B)

Using standard normal table,

P(Z < z) = 65%

= P(Z < z) = 0.65

= P(Z <0.39 ) = 0.65

z =0.39

Using z-score formula  

x= z * +

x= 0.39*2.3+5.8

x= 6.697

x=7

(C)

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 2.3+5.8

x = 4.24865

x=4