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2-3 Normal Distribution
Normal • A normal distribution is modeled by a bell-
shaped curve called a normal curve that is symmetric about the mean.
• A normal distribution with mean and standard deviation has the following properties. The total area under the related normal curve is 1.
x
• The percent of the area covered by each standard deviation is shown in the graph.
1
68
95
99.7
𝑥 𝑥 +2𝜎
34% 13.5% 47.5%
13.5% + 2.35% + 0.15% = 16%
a. The scores of 518 and 748 represent 2 standard deviations to the right of the mean. So, the percent of the test-takers that have scores between 518 and 748 is 34% + 13.5% = 47.5%.
b. A score of 403 is 1 standard deviation to the left of the mean. So, the percent of the test-takers that have scores less than 403 is 13.5% + 2.35% + 0.15% = 16%.
Standard Normal Distribution
x xz
58 − 64.5
2.5 -2.6
-2.6 -2.6 0.0047
.47%
34% + 34% = 68%
𝑍 =70−64.5
2.5=2.2, so 0.9861 or 98.61% is the
probability.
NTG Page 248 #1 - 21