Question

A set of data with 1200 numbers is normally distributed with a mean of 27 and a standard deviation of 4. How many numbers in the data would you expect to be between 23 and 31?

What numbers would be between 19 and 35 as well?
Help!

Answer 1

Explanation:

The mean is 27 and the standard deviation is 4.

23 is 1 standard deviation below the mean, and 31 is 1 standard deviation above the mean. According to the empirical rule, 68% of the population is between -1 and +1 standard deviations.

68% of 1200 is 816.

19 is 2 standard deviations below the mean, and 35 is 2 standard deviations above the mean. According to the empirical rule, 95% of the population is between -2 and +2 standard deviations.

95% of 1200 is 1140.