Question

The sat mathematics score in the state of florida for this year are approximately normally distributed with a mean of 500 and standerd 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 decima.

Answer 1

Since $700=500+2\times100=\mu+2\sigma$ is 2 standard deviations above the mean, you're looking for the probability that

$\mathbb P(0$

The empirical rule says that approximately 95% of a normal distribution lies within 2 standard deviations of the mean, or $\mathbb P(|Z|$.

Since the normal distribution is symmetric, you have

$\mathbb P(|Z|$