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. Usng 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

0.006 probability as 0.003 is either side of the mean.

Explanation:

The empirical rule is a percentage representative of 68–95–99.7 rule.

When we transfer the figures to the mean we can precisely estimate that if the mean is 500 then the empirical rule can operate either side to the mean as long they stay together each side of the mean.

Then the percentages would represent the following

If the lowest mass value was 400 and the highest mass value was 600 then 68% of that mass would be accounted for but it would be arguable that 95-99.7% of that mass would be accounted for unless we were given the standard deviation. As standard means whole. The answer therefore is reliable and the 68% would be the inverse of 68 = 32 +- the mean as first step 32% = 0.32

Probability is inverse of 99.7%+99.7% = 0.003+0.003 = 0.006%= 0.006 this shows the mass of a subject so the probability of finding within 200% either side therefore gets doubled again as 99.7% of 200 = 0.6

but doubled is 99.7% of 400 is 399.12 which makes the decimal inverse 0.3/100 12/400= 0.03, but as we account for standard deviation we can then ignore this amount and only account for 0.003/100 either side.