Chapter 2 2:2 Density Curves and Normal Distribution

Density curve

1) Is always on or above the horizontal axis

1) has an area exactly 1 underneath it

What do Density Curves tell us?

1) describes overall pattern of a distribution

2) area under the curve estimates the proportion of all observations that fall in the interval

3) curve won’t be perfectly drawn

What does the median of a Density Curve show us?

1) the equal areas point

2) the point that divides the area under the curve in half

What does the mean of a Density Curve show us?

1) point at which curve would balance

Where are the mean and median for a symmetric Density Curve?

center of curve

The _____ of a skewed curve is pulled away from the ______ in direction of the long tail?

1) mean

2) median

What is the symbol for mean of a density curve?

μ, Greek letter mu

What is the symbol for standard deviation of a density curve?

σ, Greek letter sigma

Is the mean and standard deviation symbol the same for actual observations and density curve?

no

Shape of Normal Curves

1) same overall shape

2) symmetric

3) single-peaked

4) bell shaped

Center of Normal Curves

mean and median located at the midpoint of the symmetric density curve

Variability of Normal Curves

The standard deviation σ measures the variability (width) of a Normal distribution

What does the standard deviation show in a Normal Curve?

the distance from the center to the change-of-curvature points on either side

When drawing a Normal Curve, abbreviate with….

N(μ,σ)

For Normal Distributions, approx. ____ of the observations fall within ____ standard deviation of the mean

1) 68%

2) one

For Normal Distributions, approx. ____ of the observations fall within ____ standard deviation of the mean

1) 95%

2) two

For Normal Distributions, approx. ____ of the observations fall within ____ standard deviation of the mean

1) 99.7%

2) three

What is the mean and standard deviation in a Normal Distribution?

1) mean = 0

2) standard deviation = 1

To find the z- score or standardized variable of a Normal Distribution, do…

z= (value-μ)/σ

Rule for Normal Distribution

68-95-99.7 rule