Chapter 2: Density Curves and Normal Distributions. Density Curves. What is the probability of scoring in one of these regions? What do all of the areas of the rectangles add up to be? What do all of the probabilities add up to be?. Density Curves.
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What is the probability of scoring in one of these regions?
What do all of the areas of the rectangles add up to be?
What do all of the probabilities add up to be?
Skewed Right Density Curve Skewed Left Density Curve
Skewed right – mean to the right of the median.
Skewed left – mean to the left of the median.
Centered at the mean.
Positive standard deviations are data to the right of the mean, data greater than the mean.
Negative standard deviations are data to the left of the mean, data less than the mean.
Approximately 68% of the data falls within one standard deviation to the left and right of the mean.
Approximately 95% of the data falls within two standard deviations to the left and right of the mean.
Approximately 99.7% of the data falls within three standard deviations to the left and right of the mean,
We can standardize data set, so that each data point is represented by number of standard deviations from the mean.
The level of cholesterol in the blood is important because high cholesterol levels may increase the risk of heart disease. The distribution of blood cholesterol levels in a large population of people of the same age and sex is roughly normal. For 14 year old boys the mean is μ=170 mg of cholesterol per dl of blood (mg/dl)and the standard deviation is σ=30 mg/dl. Levels above the 240 mg/dl may require medical attention. What percent of 14 year old boys have more than 240 mg/dl of cholesterol?
Step 2: Use the Table. Look in Table A for the entry closest to .9 since that would be the area to the left of our .1 region.
z = 1.28 is our standardized score.