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

The answer is 0.95

Explanation:

Under the empirical rule, or the three sigma rule or 68-95-99.7 rule, as given in the question 300 and 700 are two standard deviations from the mean 500. So, the probability that a randomly selected students math score is between 300 and 700 is 0.95.

Answer 2

Using the empirical rule, the probability that a randomly selected student's math score is between 300 and 700 (both 2 standard deviations below the mean) is 95%. Or in decimal form, .95.