Question

Find the area to the left of x=73 under a normal distribution curve with mean=71 and standard deviation =2 .Round your answer to four decimal places.

Answer 1

To find the area to the left of x=73 under a normal distribution curve:

1. Find the corresponding z, use the next formula:

$z=\frac{(x-\operatorname{mean})}{\text{standard deviation}}$$\begin{gathered} z=\frac{73-71}{2} \\ \\ z=\frac{2}{2} \\ \\ \\ z=1 \end{gathered}$

2. Find the z-score corrsponding to z=1, use a z score table:

The area to the left of z is equal to the corresponding z-score.

Then, the area to the left of x=73 is 0.8413