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.

The answer is 0.95

Step-by-step 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.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.