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 5.4, with a standard deviation of 2.3.
(a) What response represents the 86th percentile? (Round to two decimal places as needed).
​(b) What response represents the 55th ​percentile? (Round to two decimal places as needed).
​(c) What response represents the first ​quartile? (Round to two decimal places as needed).

Answer 1

The response that represents the 86th percentile is 7.884

The response that represents the 55th percentile is 5.69

The response that represents the first percentile 3.85

How to solve for the 86th percentile

mean = 5.4

sd = 2.3

p(X>x) = 0.86

find the value of z using the NORMSINV function in excel with a probability of 0.86

z = 1.080

x = mean + sd*z

= 5.4 + 2.3 * 1.080

= 7.88

How  to solve for the 55th percentile

mean = 5.4

sd = 2.3

p(X>x) = 0.55

find the value of z using the NORMSINV function in excel with a probability of 0.55

z = 0.1257

x = mean + sd*z

= 5.4 + 2.3 * 0.1257

= 5.69

c. The first quartile is 25%

z = -0.6745

5.4 + 2.3 * -0.6745

= 5.4-1.551

= 3.85

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