Question

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.

Answer 1

GIVEN

The following values are given:

`\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}`

SOLUTION

The z-score for the x values 9 and 14 can be calculated using the formula:

`z=(x-\mu)/(\sigma)`

For x = 9:

`\begin{gathered} z=(9-10.3)/(3.8) \\ z=-0.34 \end{gathered}`

For x = 14:

`\begin{gathered} z=(14-10.3)/(3.8) \\ z=0.97 \end{gathered}`

The probability can be calculated as follows:

`P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:<p>Therefore, the probability is given to be:</p>[tex]P(9\le x\le14)=0.4671`

The probability is 0.4671.