Stats 330 Exam 2 April 3 Flashcards
What are the requirements for a binomial experiment?
1) The experiment must have a fixed number of trials.
2) The trials must be independent.
3) Each trial must have all outcomes classified into two categories.
4) The probabilities must remain constant for each trial.
How many outcomes are possible in a binomial experiment?
Two possible outcomes
What two categories are used in binomial distribution?
S= a success with P(S)=p F= a failure with P(F)= 1-p = q
What does P(x<=n) always equal?
1.0
When does a continuous random variable, X, have a normal distribution?
If the distribution is symmetric and bell shaped then it has a normal distribution.
What notation is used to denote that a random variable has a normal distribution?
X ~N(mu, sigma^2)
What is the mean and st dev of the standard normal distribution?
mean of 0, standard deviation of 1, also called the Z distribution Z~N(0,1)
What are the characteristics of the standard normal distribution?
- ) The standard normal distribution is symmetrical and bell shaped.
- ) It is symmetrical about the mean 0.
- ) The empirical rules apply to this distribution.
- ) We can find the probability that z equals a specified value by using a table.
What does greater than mean?
area to the right
What does less than mean?
area to the left
How do we find percentiles in the standard normal distribution?
by using the table in a backward direction
What is the 50%ile equal to?
it is equal to 0 or the mean
How many digits should you round to?
4 digits
Central Limit Theorem
1) the distribution of sample means xbar will, as the sample size increases, approach a normal dist.
2. ) The mean of the sample means will be the pop mean mu.
3. ) The st dev of the sample means will be sigma/square root of n
What is the mean of the sample mean?
mu_xbar
What is the probability distribution of the sample mean?
mu_xbar=?
sigma_xbar=? or sigma^2_xbar=?
If x is normal, then xbar has a _______?
normal distribution
If x is not normal, then xbar has a normal distribution if ____?
n>29
How do you find P(xbar>b)?
Z=xbar-mu/sigma over square root of n
How many nonstandard normal distributions are there?
there are an infinite number of nonstandard normal distributions
What is a random variable that has a nonstandard normal distribution?
It is a random variable that has a normal distribution with a mean mu and a standard deviation sigma.
What is the notation for a nonstandard normal distribution?
X~N(mu,sigma^2)
How do you find P(x>a)?
First convert x to z then find P(Z>k)
What is Z_alpha?
alpha represents the area to the right of z
How do you solve a nonstandard normal dist problem?
- ) operation standardization
- ) write what expressions are equal to
- ) go to standard normal table
Estimator
A sample statistic used to approximate a population parameter
Point Estimate
a single value used to approximate a population parameter
Sample mean (xbar)
the best point estimate of the population mean mu
Sample variance (S^2)
the best point estimate of the population variance sigma^2
Confidence interval
a range of values that is likely to contain the true value of the population parameter
Degree of confidence
the probability 1-alpha that the confidence interval contains the true value of the population parameter
