Google Classroom
GeoGebraGeoGebra Classroom

Normal distribution

The figure below will help you to visualize the 68-95-99.7 Rule (or the Empirical Rule) for a Normal Distribution. The histogram displays 100 data values from a population N(0,1). The histogram is centered on the mean of the data. The width of each bin is the standard deviation of the data. Therefore, the bin boundaries are z-scores. The numbers on each bin is the number of data values in the bin. Since there are 100 data values, these numbers are percents.

Empirical rule practice

1. For the distribution N(155, 9), use the empirical rule (68-95-99.7 rule) to determine the percent of data values between 138 and 155.

Practice Area under the curve.

2. What is the percentage of a normal distribution that is less than the mean?

Normal Distribution Practice Problems

3. For a normal model with mean 9.7 and a standard deviation of 1.2, what proportion of data values are greater than 10?

4. The age of student in a community college is normally distributed with a mean of 30 years and standard deviation σ = 4 years. Let X represent the age of a randomly selected student. Find a) P(x < 40)  b) P(x > 21)  c) P(30 < x < 35) 

5. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?