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?

Answer 1

Hello, thank you for taking the time to post your question!

The Empirical Rule says that 95% of values lie within 2 standard deviations of the mean. That means that 95% of values on this one lie between 500 – 2(100) = 300 and 500 + 2(100) = 700.

Since the question is asking about the chance of the value being between 500 and 700 it would just be half of 95%, since we only have the upper part of the interval.

That means the final calculation is 95% / 2 = 47.5% of the values lie between 500 and 700.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)