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 with a mean of 45 and a standard deviation of 3.5. 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
45-3( 3.5)
45-2( 3.5)
45- 3.5
45
45+ 3.5
45+2( 3.5)
45+3( 3.5)
Simplify
34.5
38
41.5
45
48.5
52
55.5
Now, let's draw vertical lines 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, 45. The values of the normal curve that are 3 standard deviations away from the mean should be close to 0.
To make the graph look cleaner, we can erase the parts of the vertical lines that are above the curve.
