The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100

Question

The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100.Using the empirical rule, what is the probability that a randomly selected student�s math score is between 300 and 700? Express your answer as a decimal.

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Sadie 5 days 2021-10-14T13:23:16+00:00 1 Answer 0

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    2021-10-14T13:24:47+00:00

    Answer:

    Step-by-step explanation:

    The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below

    68% of data falls within the first standard deviation from the mean.

    95% fall within two standard deviations.

    99.7% fall within three standard deviations.

    From the information given, the mean is 500 and the standard deviation is 100.

    95% of the scores of students would fall within two standard deviations.

    2 standard deviations = 2 × 100 = 200

    500 – 200 = 300

    500 + 200 = 700

    Therefore, the probability that a randomly selected student math score is between 300 and 700 is

    95%

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