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.

Since the range of the scores given was between 300 and 700 (which is 2 standard deviations below and above the mean), the probability that a randomly selected student's math score - as based on the empirical rule of statistics - is 95%. In decimal form, it is .95.

Answer Link

joaobezerra joaobezerra · Answer 2 · 2022-03-24T06:54:45-04:00

Using the Empirical Rule, it is found that there is a 95% probability that a randomly selected student’s math score is between 300 and 700.

What is the Empirical Rule?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, considering the mean of 500 and the standard deviation of 100, scores between 300 and 700 are within 2 standard deviations of the mean, hence, there is a 95% probability that a randomly selected student’s math score is between 300 and 700.

To learn more about the Empirical Rule, you can check https://brainly.com/question/24537145