Question

(1 point) Suppose 2' is a normally distributed random variable with u = 10.3 and 0 = 3.8. For the following probability,draw an appropriate diagram, shade the appropriate region and then determine the value:P(9 < 2 ≤ 14) =

Answer 1

Recall the z score formula:

In this case:

$\mu=10.3\text{ and }\sigma=3.8$

Therefore:

$z=\frac{x-\mu}{\sigma}$

Calculate the z score for x = 9:

$\begin{gathered} z_1=\frac{9-10.3}{3.8} \\ z_1=-0.3421 \end{gathered}$

Similarly, the z score of 14 is:

$z_2=\frac{14-10.3}{3.8}=0.9737$

The required diagram is shown.

And the required probability:

P(9 ≤ x ≤ 14) = P(-0.3421 ≤ z ≤ 0.9737) =

Therefore, the correct answer is:

0.4688.