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Scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be less than 70? Show your work.

Answer :

In order to find the probability, first let's calculate the z-score for x = 70, using the formula below:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ z=\frac{70-81}{8}\\ \\ z=-\frac{11}{8}\\ \\ z=-1.375 \end{gathered}[/tex]

Now, let's look at the z-table for the probability that corresponds to z = -1.375.

Looking at the z-table, for z = -1.375 we have p = 0.0845.

Therefore we have:

[tex]P(x<70)=P(z<-1.375)=0.0845=8.45\%[/tex]

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