Could someone help me with statistics

The numbers of cookies in a shipment of bags are normally distributed, with a mean of 48 and a standard deviation of 5. What percent of bags of cookies will contain between 38 and 58 cookies?

The answer is 95%. Could someone help me understand how to get the answer? Thank you!

Meg -

This problem is testing your knowledge of the "Empirical Rule" which states that 95% of the data is within 2 standard deviations of the mean:

mean +/- 2(standard deviation) = 48 +/- (2)(5) = 48 +/- 10 = 38 to 58 cookies

Hope that helps

There are three critical values for percentages of observations under a normal curve that you are likely being asked to memorize:

Approximately 68% of observation in a normal distribution are within 1 standard deviation of the mean.
Approximately 95% are within 2 standard deviations
Approximately 99% are within 3 standard deviations

In order to apply this knowledge you should begin these problems by calculating how many standard deviations the observations are from the mean. You can use either of the boundaries, but I'll use the upper bound. Simply take the difference of the boundary and the mean, and divide it by standard deviation:

(58-48)/5=2

And then from the above three values that you need to memorize, you mentally "lookup" 2 and see that 95% should lie within those two values.