Probability density function (pdf)
an equation used to compute probabilities of continuous random variables
Two properties the probability density function must satisfy
1.) The total area under the graph of the equation over all possible values of the random variable must equal 1.
2.) The height of the graph of the equation must be greater than or equal to 0 for all possible values of the random variable.
Normal curve
relative frequency histograms that are symmetric and bell-shaped are said to have this shape
Properties of the Normal Density Curve
1. It is symmetric about its mean
2. Because mean = median = mode, there is a single peak at the mean
3. It has inflection points at 1 standard deviation of the mean
4. The area under the curve is 1
5. The area under the curve to the right of the mean and
Sampling distribution
a probability distribution for all possible values of the statistic computed from a sample size n
Sampling distribution of the sample mean
x?, the probability distribution of all possible values of the random variable x? computed from a sample of size n from a population with mean and standard deviation
Standard error of the mean
the standard deviation of the sampling distribution of x?, denoted ?x??
The Central Limit Theorem
Regardless of the shape of the underlying population, the sampling distribution of x? becomes approximately normal as the sample size, n, increases
Sample proportion
denoted p� (read p-hat) is given by p�= x/n
Shape
As the size of the sample, n, increased, this becomes approximately normal
Center
The mean of the sampling distribution of the sample proportion equals the population proportion, p
Spread
The standard deviation of the sampling distribution of the sample proportion decreases as the sample size, n, increases
1/2
The area under the normal curve to the right of u equals
inflection points on the normal curve
x = u - ?
x = u + ?
?
The notation z? is the? z-score that the area under the standard normal curve to the right of z?
?
?x equals
? / square root of n
?x equals
True or False:
The population proportion and sample proportion always have the same value
False