Question

The scores on the SAT college entrance exam are normally distributed with a mean Math score of 480 and a standard deviation of 100. If you select 50 students, what is the probability that their mean Math score is more than 520. You MUST show what went into the calculator along with your final answer rounded correctly to 3 significant decimal places.

Answer 1

Let X denote the Math scores on the SAT college entrance exam.

Now, we are given that:

The above statement implies that:

Thus,

Now, the probability that the mean math score is more than 520 is given by:

What went into the calculator depends on the type of calculator used. Generally we will enter 2.828427 and ask for it to calculate the cdf of the standard normal distribution at that point.

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