Question

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The meanresponse was 5.2 with a standard deviation of 2.4.(a) What response represents the 95th percentile?(b) What response represents the 60th percentile?(c) What response represents the first quartile?...

Answer 1

(a)

`\begin{gathered} Z-\text{score for 95 percentile = 1.645} \\ x=Z\sigma+\mu \\ x=1.645(2.4)+5.2 \\ x=9.148 \\ x=9.15\text{ (2 decimal places)} \end{gathered}`

(b)

`\begin{gathered} Z-\text{score for 60 percentile = }0.253 \\ x=Z\sigma+\mu \\ x=0.253(2.4)+5.2 \\ x=5.8072 \\ x=5.81\text{ (2 decimal places)} \end{gathered}`

(c)

`\begin{gathered} Z-\text{score for first quartile (25\%) = }-0.674 \\ x=Z\sigma+\mu \\ x=-0.674(2.4)+5.2 \\ x=3.5824 \\ x=3.58\text{ (2 decimal places)} \end{gathered}`