ST 260 Exam 2 Casselman
compute to z values
(score-mean)/standard deviation
expected value formula
(x* the probability) summed up
conditions of a binomial distribution
1) a fixed number of trials "n" 2) all n trials must be independent of each other 3) all same probability of success on each trial 4)x= count of the number of successes
areas between standard deviations
68,95,99.7
statistics
the science of decision making in the face of uncertainty
independence
two events are independent if one event does not affect the probability of another event
Bernoulli distriution
a discrete data distribution used to describe a population of binary variable values
binomial distribution
a discrete data distribution used to model a population of counts for "n" independent repetitions of a Bernoulli experiment
probability
a numerical measure of the likelihood that an event will occur
expected value
an experiment repeated many times and the average of the result
quantitative variables
averages or differences have meaning
continuous random variable
can assume any value in an interval on the real line or in a collection of intervals
three methods for assessing probability
classical, relative frequency, subjective
categorical variables
classify people or things
normal probability distribution standard deviation
determines width of the curve- larger deviation results in wider and flatter curves
statistical inference
generalizing from a sample to a population, by using a statistic to estimate a parameter
sampling distribution of x
is the distribution of all possible sample means calculated from all possible samples of size n also called the population of all possible x bars
pi=
mean
standard normal distribution
mean =0 and standard deviation=1
bigger variance=
more risk
probability requirements for discrete variables
must be between zero and 1 P(A)=0 imposible P(A)=1 certain sum up probabilities of all possible outcomes must equal 1
mean of a binomial distribution
n(pi)
z=
number of standard deviations that an x value is from the mean
a fair bet
one in which the expected value of the winnings is zero (don't pay more than the expected value)
binary
only one of two outcomes can occur (0 and 1)
p(a and b)
p(a)*p(b|a)
p(a or b)
p(a)+p(b)-p(a and b)
sample proportion variance
pi(1-pi)/n
confidence interval
point estimate +/- margin of error
if the true population standard deviation is known
replace sigma with s replace z with t
standard error of a sampling distribution
sigma/sqrt(n)
standard deviation
sqrt(npi(1-pi))
standard deviation of bernoulli
sqrt(pi(1-pi))
standard deviation expected value
square root of variance
variance expected value
sum of (x-expected value)^2 *p
as n-1 increases
t sub n-1 approaches z
conditional probability
the chance one event will happen given another event will occur p(a and b)/p(b)