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Fed [463]
1 year ago
9

5#The distribution of scores on a standardized aptitude test is approximately normal with a mean of 480 and a standard deviation

of 105. What is the minimum score needed to be in the top 20% on this test? Carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.
Mathematics
1 answer:
kirza4 [7]1 year ago
7 0

We want to find the value that makes

P(X\ge x)=0.2

To find it we must look at the standard normal table, using the complementary cumulative table we find that

P(Z\ge z)=0.20045\Leftrightarrow z=0.84

Then, using the z-score we can find the minimum score needed, remember that

z=\frac{x-\mu}{\sigma}

Where

σ = standard deviation

μ = mean

And in our example, x = minimum score needed, therefore

\begin{gathered} 0.84=\frac{x-480}{105} \\  \\ x=0.84\cdot105+480 \\  \\ x=568.2 \end{gathered}

Rounding to the nearest integer the minimum score needed is 568, if you get 568 you are at the top 20.1%.

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