Answer:
[tex]Area=0.0228\text{ or 2.28\%}[/tex]Explanation:
We were given the following information:
This is a normal distribution curve
Mean = 53
Standard deviation = 9
We are to find the area right of x = 71
This is calculated as shown below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=71 \\ \mu=53 \\ \sigma=9 \\ \text{Substitute these into the formula, we have:} \\ z=\frac{71-53}{9} \\ z=\frac{18}{9} \\ z=2 \end{gathered}[/tex]We will proceed to plot this on a graph as sown below:
The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:
[tex]\begin{gathered} =1-0.9772 \\ =0.0228 \\ =2.28\text{\%} \end{gathered}[/tex]Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%
