Chapter 2 . Density Curves and Normal Distributions. Remember. ALWAYS plot data (usually histogram or stemplot ) Overall Pattern (CUSS) Calculate Numerical Summary NEW – Sometimes overall pattern is so regular it can be described by a smooth curve (called a density curve) fig 2.2 pg78.
Density Curves and Normal Distributions
20% , the region is a rectangle with height of 1 and base width of 0.2
Mean = ½ or 0.5, the ‘balance point’ of the density curve
Find percentiles for the following heights
This quiz will go in the grade book so be sure to look over your notes and examples in the book.
If x is an observation from a distribution that has mean µ and standard deviation σ, the standardized value of x is
Standardized value is often called the z-score
Z-score tells you how many standard deviations the original observation (x) falls away from the mean (µ) and in which direction
Z = = = 1.4
What proportion of all young women are less that 68 inches tall?
How to use table A to find the proportions of observations from the standard normal distribution that are greater than a specific z-score:
z = -2.15
Find -2.15 on the left hand column and .05 in the top row…. The table entry is 0.0158. This means that the area to the left of -2.15 is 0.0158. Since the total area under the curve is equal to 1, the area lying to the right of -2.15 is:
1 - 0.0158 = 0.9842
Figure 2.16 on page 97 illustrates these areas.
How to find a value when given the proportion, and .
You will need to know how to solve the problem both ways!!!!
Example 2.8 on Pg. 99