The empirical rule for the normal distribution states that the distribution is symmetric around the mean (which is also the median and the mode for this distribution) and that approximately 68% of the data in the distribution falls within 1 standard deviation either way of the mean, approximately 95% of the data falls within 2 standard deviations either way of the mean, and approximately 99.7% of the data falls within 3 standard deviations either way of the mean.
Use the empirical rule to solve the examples below.
1. 300 biology students take a midterm exam. The distribution of their scores is approximately normal. Find the number of scores
a. within 1 standard deviation of the mean
b. within 2 standard
deviations of the mean
2. The SAT-M test has a distribution which is approximately normal, with mean = 500 and standard deviation = 100. Find the percent of people taking the SAT-M test whose scores fall in these categories:
a. more than 500
b. more than 600
c. more than 700
d. between 400 and 600
e. between 300 and 500
f. between 300 and
600
3. In a certain area in the west, the average motorist drives about 1200 miles per month, with a standard deviation of 150 miles. Assume that miles driven in this area can be approximated by the normal curve. Find the percent of motorists who
a. drive more than 1350 miles per month
b. drive less than 1350 miles per month
c. drive less than 900 miles per month
d. Of 500 motorists
from this area, how many would you expect to drive less than 900 miles
per month?