In the lab #5, question 1e “How much would a student score if he/she were in the top 10% of population scores? Show your work’’. That is a backward probability. In this case we already have the probability and what we want is which value of the give us that probability. That is, we have \(P(X > ?) = 0.10\) and we want to know what”?" is. First thing to do to help understand the problem is draw the curve:

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Therefore, we want x so that

\[ P(X > x) = .10 \]

And that is the same as

\[ P(X < x) = 1 - P(X > x) = 0.90 \]

We don’t have a table for a Normal distribution with mean 42 and standard deviation 16, but we do have one for a standard normal distribution (that is, a normal distribution with mean 0 and standard deviation 1). So, looking inside the the table, we can find that the

\[ P(Z < 1.28) = 0.90 \]

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We also know that

\[ z = \dfrac{x - \mu}{\sigma} = \dfrac{x - 42}{16} \]

Then,

\[ 1.28 = \dfrac{x - 42}{16} \]

Solving the equation we have that \(x=62.48\).