A normal curve is bell-shaped and the highest point of the curve is at the mean.
Practice makes perfect
We will sketch a normal curve that represents an experiment with a mean of 180 and a standard deviation of 15. First, let's find the values that are one, two, and three standard deviations away from the mean. For convenience, the mean will be represented by the letter m and the standard deviation will be represented by s.
m-3s
m-2s
m-s
m
m+s
m+2s
m+3s
Substitute
180-3( 15)
180-2( 15)
180- 15
180
180+ 15
180+2( 15)
180+3( 15)
Simplify
135
150
165
180
195
210
225
Now, let's draw vertical lines and label the x-axis with the calculated values.
Finally, we can sketch the normal curve. Let's draw a bell-shaped curve with its highest point at the mean, 180. The values of the normal curve that are 3 standard deviations away from the mean should be close to 0.
The normal curve is divided into sections of standard deviation widths. Let's label the percentages of each section.
The percentage of each section indicates a probability that the resulting value of the experiment will end up in the corresponding section.
