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 5.2 with a standard deviation of 2.6. ​(a) What response represents the 94th ​percentile? ​(b) What response represents the 61st ​percentile? ​(c) What response represents the first ​quartile?

Answer 1

Solution :

Given that,

mean = = 100

standard deviation = = 2.6

a ) P(Z < z) = 94%

= P(Z < z) = 0.94

= P(Z < 1.55 ) = 0.94

z = 1.55

Using z-score formula,

x = z * +

x = 1.55 * 2.6+5.2

x = 9.23

94^th ​percentile = 9.23

b ) P(Z < z) = 61%

= P(Z < z) = 0.61  

= P(Z < 0.28 ) = 0.61

z = 0.28

Using z-score formula,

x = z * +

x = 0.28 * 2.6+5.2

x = 5.928

61^st ​percentile = 5.93

c ) P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 2.6+5.2

x = 3.458

first ​quartile = 3.46