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 5.9 with a standard deviation of 2.2. ​(a) What response represents the 92nd ​percentile? ​(b) What response represents the 60th ​percentile? ​(c) What response represents the first ​quartile?..

Answer 1

Solution:-

Given that,

mean = = 5.9

standard deviation = = 2.2

Using standard normal table,

a) P(Z < z) = 92%

= P(Z < z ) = 0.92

= P(Z < 1.4051 ) = 0.92  

z = 1.4051

Using z-score formula,

x = z * +

x = 1.4051 * 2.2 + 5.9

x = 8.99

b) P(Z < z) = 60%

= P(Z < z ) = 0.60

= P(Z < 0.2534 ) = 0.60  

z = 0.2534

Using z-score formula,

x = z * +

x = 0.2534 * 2.2 + 5.9

x = 6.46

Using standard normal table,

c) 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 * 2.2 + 5.9

x = 4.42

First quartile =Q1 = 4.42