![[SOLVED] Suppose 2' is a normally distributed random variable with ft = 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) = Note: Enter your answer up to 4 decimal places.](https://us-static.z-dn.net/files/d5a/0995fdaa02aeca5b20d6cc27ca7be83b.png "[SOLVED] Suppose 2' is a normally distributed random variable with ft = 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) = Note: Enter your answer up to 4 decimal places.")
GIVENThe following values are given:[tex]\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}[/tex]SOLUTIONThe z-score for the x values 9 and 14 can be calculated using the formula:[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 9:[tex]\begin{gathered} z=\frac{9-10.3}{3.8} \\ z=-0.34 \end{gathered}[/tex]For x = 14:[tex]\begin{gathered} z=\frac{14-10.3}{3.8} \\ z=0.97 \end{gathered}[/tex]The probability can be calculated as follows:[tex]P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:Therefore, the probability is given to be:[tex]P(9\le x\le14)=0.4671[/tex]The probability is 0.4671.
