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Tom Lowbridge · Answer 1 · 2023-05-26T09:59:32+0000

The following parameters are provided in the question:

$\begin{gathered} x=75 \\ \mu=82 \\ \sigma=5 \end{gathered}$

First, we will calculate the z-score:

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

Substituting, we have:

$\begin{gathered} z=(75-82)/(5)=(-7)/(5) \\ z=-1.4 \end{gathered}$

The distribution curve and the area that represents the probability is shown below:

Therefore, the probability is calculated to be:

$P(x<75)=Pr(z<-1.4)=Pr(Z<0)-Pr(0Using the area under the normal curve calculator, we have that:[tex]\begin{gathered} Pr(Z<0)=0.5 \\ Pr(0<strong>Therefore, the probability will be:</strong>[tex]\begin{gathered} P(x<75)=0.5-0.4192 \\ \therefore \\ P(x<75)=0.0808 \end{gathered}$

assume the random variable x is normally distributed with mean =82 and standard deviation-example-1

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