Unit 7, Lesson 7
Areas under a Normal Curve
Integrated Math 3
7.1
Warm-up
The images show a normal curve with mean of 40 and standard deviation of 2.
The area under the curve to the left of 39 is 0.3085.A bell-shaped distribution with the horizontal axis labeled from 36 to 46 by 2s. The peak of the bell is centered at 40. The vertical axis labeled from 0 to 0.20 by 0.05’s. The area under the curve is shaded through a vertical line at 39.
The area under the curve to the left of 43 is 0.9332.Graph of normal curve. Horizontal axis from 34 to 46 by 2’s. Vertical axis from 0 to point 2 by point 0 5’s. Curve peaks near point 1 2. Area under curve is shaded from 34 to 43.
Since it is a normal curve, we know that the total area under the curve is 1. Use the given areas to find the areas in question. Explain your reasoning for each.
- Find the area under the curve to the right of 39.
- Find the area under the curve between 39 and 43.
- Find the area under the curve to the left of 40.
- Find the area under the curve between 39 and 40.