Empirical Rule Practice

What percent of the data lies OUTSIDE of three standard deviations of the mean?

The heights of female students in J.K. High School are normally distributed with a mean of 66 inches. If 95% of the heights of these students fell between 63 and 69 inches, what is the standard deviation for this set of data?

A distribution is normally distributed. What percent of the data falls OUTSIDE three standard deviations of the mean?

500 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and standard deviation of 4. Approximately how many juniors scored between 24 and 28?

The actual weights of bags of pet food are normally distributed. The mean of the weights is 50 lbs with a standard deviation of 0.2 lbs. In a group of 250 bags, how many would you expect to weigh more than 50.4lbs?

In the image, the shaded area represents approximately 95% of the scores on a test. If these scores ranged from 78 to 92, what is the mean?

A machine is used to put bolts into boxes. It does so much that the actual number of bolts in a box is normally distributed with a mean of 106 and a standard deviation of 2. What percentage of boxes contain less than 108 bolts?

The heights of people on Mars are normally distributed with a mean of 40 and a standard deviation of 5. 16% of the Martians are over how many inches tall?

The lifetime of batteries is normally distributed for large samples. The mean lifetime if 500 days and the standard deviation is 61 days. Approximately what percent of batteries have lifetimes longer than 622 days?

A test was given to 120 students, and the scores approximated a normal distribution. If the mean score was 72 with a standard deviation of 7, approximately how many students had scores higher than 65?