Recall the z score formula:
In this case:
[tex]\mu=10.3\text{ and }\sigma=3.8[/tex]
Therefore:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Calculate the z score for x = 9:
[tex]\begin{gathered} z_1=\frac{9-10.3}{3.8} \\ z_1=-0.3421 \end{gathered}[/tex]
Similarly, the z score of 14 is:
[tex]z_2=\frac{14-10.3}{3.8}=0.9737[/tex]
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.
