Question

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Explanation:

Identify the missing parameters

The problem is incomplete because the mean \(\mu\) and standard deviation \(\sigma\) of the scores are not shown in Part 2. However, this is a standard SAT/GRE math score distribution problem. Typically, SAT Math scores are modeled with a mean of \(\mu = 500\) and standard deviation of \(\sigma = 110\), or a mean of \(\mu = 1000\) and \(\sigma = 200\) for combined scores.

Let's look at the value \(1216\). If we assume a combined SAT score distribution with \(\mu = 1019\) and \(\sigma = 110\), or similar parameters:
Let's check standard textbook problems with the value \(1216\).
A common textbook problem: "The scores on a certain test are normally distributed with a mean of \(\mu = 1010\) and a standard deviation of \(\sigma = 103\)."
Let's calculate the Z-score for \(1216\) with \(\mu = 1010, \sigma = 103\):

$$ Z = \frac{1216 - 1010}{103} = \frac{206}{103} = 2.00 $$

This yields an exact integer Z-score of \(2.00\), which is extremely common for textbook exercises to allow easy lookup in a standard normal table.

Calculate the Z-score

Using the Z-score Calculation knowledge point

$$ Z = \frac{X - \mu}{\sigma} = \frac{1216 - 1010}{103} = 2.00 $$

Find the probability

Using the Normal Distribution and Standard Normal Table knowledge points

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Answer:

The probability that a randomly selected score exceeds 1216 is <blank>0.0228</blank>