http://www.ck12.org Chapter 6. Normal Distribution Curves
- What percentage of the data in a normal distribution is between 2 standard deviations below the mean and 3
standard deviations above the mean? - What percentage of the data in a normal distribution is between 3 standard deviations below the mean and the
mean? - What percentage of the data in a normal distribution is more than 1 standard deviation above the mean?
- What percentage of the data in a normal distribution is between the mean and 2 standard deviations above the
mean? - 200 senior high students were asked how long they had to wait in the cafeteria line for lunch. Their responses
were found to be normally distributed, with a mean of 15 minutes and a standard deviation of 3.5 minutes. (a)
How many students would you expect to wait more than 11.5 minutes? (b) How many students would you
expect to wait more than 18.5 minutes? (c) How many students would you expect to wait between 11.5 and
18.5 minutes? - 350 babies were born at Neo Hospital in the past 6 months. The average weight for the babies was found to
be 6.8 lbs, with a standard deviation of 0.5 lbs. (a) How many babies would you expect to weigh more than
7.3 lbs? (b) How many babies would you expect to weigh more than 7.8 lbs? (c) How many babies would you
expect to weigh between 6.3 and 7.8 lbs? - Sheldon has planted seedlings in his garden in the back yard. After 30 days, he measures the heights of the
seedlings to determine how much they have grown. The differences in heights can be seen in the table below.
The heights are measured in inches. Draw a normal distribution curve to represent the data. Determine what
the range of the differences in heights of the seedlings is for the middle 68% of the data.
10 3 8 4 7 12 8 5 4 9 3 8
6 10 7 10 11 8 12 9 10 7 8 11
Summary
This chapter covers describing in detail the spread of a normal (bell-shape) distribution. Thestandard deviationis a
measure of how spread out the data is. It is represented asσfor a population orsfor a sample. Ifxis a data value,μ
andxare the mean, andnis number of data values, then the standard deviation is:
σ^2 =∑(x−μ)
2
n (population) or s(^2) =∑(x−x)^2
n− 1 (sample)
The only difference in the formulas is the number by which the sum is divided. The standard deviation found by this
method defines the spread of the curve. TheEmpirical Ruleor68-95-99.7 Ruledefines how much of the distribution
is within 1, 2, and 3 standard deviations of the mean.