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.

Answer 1

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%