Stats 330 Exam 2 April 3

Question 1

What are the requirements for a binomial experiment?

Answer 1

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.

Question 2

How many outcomes are possible in a binomial experiment?

Answer 2

Two possible outcomes

Question 3

What two categories are used in binomial distribution?

Answer 3

S= a success with P(S)=p
F= a failure with P(F)= 1-p = q

Question 4

What does P(x<=n) always equal?

Answer 4

1.0

Question 5

When does a continuous random variable, X, have a normal distribution?

Answer 5

If the distribution is symmetric and bell shaped then it has a normal distribution.

Question 6

What notation is used to denote that a random variable has a normal distribution?

Answer 6

X ~N(mu, sigma^2)

Question 7

What is the mean and st dev of the standard normal distribution?

Answer 7

mean of 0, standard deviation of 1, also called the Z distribution Z~N(0,1)

Question 8

What are the characteristics of the standard normal distribution?

Answer 8

1. ) The standard normal distribution is symmetrical and bell shaped.
2. ) It is symmetrical about the mean 0.
3. ) The empirical rules apply to this distribution.
4. ) We can find the probability that z equals a specified value by using a table.

Question 9

What does greater than mean?

Answer 9

area to the right

Question 10

What does less than mean?

Answer 10

area to the left

Question 11

How do we find percentiles in the standard normal distribution?

Answer 11

by using the table in a backward direction

Question 12

What is the 50%ile equal to?

Answer 12

it is equal to 0 or the mean

Question 13

How many digits should you round to?

Answer 13

4 digits

Question 14

Central Limit Theorem

Answer 14

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

Question 15

What is the mean of the sample mean?

Answer 15

mu_xbar

Question 16

What is the probability distribution of the sample mean?

Answer 16

mu_xbar=?

sigma_xbar=? or sigma^2_xbar=?

Question 17

If x is normal, then xbar has a _______?

Answer 17

normal distribution

Question 18

If x is not normal, then xbar has a normal distribution if ____?

Answer 18

n>29

Question 19

How do you find P(xbar>b)?

Answer 19

Z=xbar-mu/sigma over square root of n

Question 20

How many nonstandard normal distributions are there?

Answer 20

there are an infinite number of nonstandard normal distributions

Question 21

What is a random variable that has a nonstandard normal distribution?

Answer 21

It is a random variable that has a normal distribution with a mean mu and a standard deviation sigma.

Question 22

What is the notation for a nonstandard normal distribution?

Answer 22

X~N(mu,sigma^2)

Question 23

How do you find P(x>a)?

Answer 23

First convert x to z then find P(Z>k)

Question 24

What is Z_alpha?

Answer 24

alpha represents the area to the right of z

Question 25

How do you solve a nonstandard normal dist problem?

Answer 25

1. ) operation standardization
2. ) write what expressions are equal to
3. ) go to standard normal table

Question 26

Estimator

Answer 26

A sample statistic used to approximate a population parameter

Question 27

Point Estimate

Answer 27

a single value used to approximate a population parameter

Question 28

Sample mean (xbar)

Answer 28

the best point estimate of the population mean mu

Question 29

Sample variance (S^2)

Answer 29

the best point estimate of the population variance sigma^2

Question 30

Confidence interval

Answer 30

a range of values that is likely to contain the true value of the population parameter

Question 31

Degree of confidence

Answer 31

the probability 1-alpha that the confidence interval contains the true value of the population parameter