Question

The SAT mathematics scores in the state of Florida for this year 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 score lies between 500 and 700? Express your answer as a decimal.

Answer 1

The empirical rule says that approximately 68% of a normal distribution falls within one standard deviation of the mean; 95% within two standard deviations; and 99.7% within three standard deviations.

The interval (500, 700) is half of the portion of the distribution that falls within two standard deviations of the mean (the whole portion being the interval (300, 700)). So, the desired probability is $0.5\times0.95=0.475$.