Question

A normal curve has μ = 20 and σ = 10. find the area between x1 = 15 and x2 = 40.

Answer 1

A normal curve has :

$\mu=20$

$\sigma=10.$

To, find the area between $X_1=15$ and $X_2=40$.

First calculate the corresponding  Z-score given by: $z=\frac{X-\mu}{\sigma}$.

$Z_1=\frac{X_1-20}{10}$$=\frac{15-20}{10}= \frac{-5}{10} =\frac{-1}{2}$

$Z_2=\frac{X_2-20}{10}$$=\frac{40-20}{10} =\frac{20}{10} =2$

Now, find the corresponding area under the standard normal curve, using the value from the standard normal distribution as shown in the attachment.

So, Area between -0.5 and 2=(Area to the right of $Z_1$)-(Area to the left of $Z_2$)

=0.3085-0.0228=0.2857