EXAM 2-Ch. 3 (2/29)

Question 1

probability

Answer 1

a value between 0 and 1, inclusive [0,1], describing the relative chance an event will occur

Question 2

probability that an event will occur=

Answer 2

number of ways the event can occur/total number of possible outcomes

Question 3

rules of probability:

Answer 3

1. prob. must be a positive real number between 0 and 1
2. prob. of 1 means the event is certain to occur (like saying 100%) and prob. of 0 means the event is certain NOT to occur
3. addition rule
4. compliment rule
5. multiplication rule
6. conditional probability

Question 4

addition rule:

Answer 4

If A and B are mutually exclusive events, then P (A or B)=P (A) + P(B)-P(A and B)

*mutually exclusive=both events can’t happen at the same time

Question 5

compliment rule:

Answer 5

a “compliment” is defined as all events NOT included in event A
P(A)=P(A’)+1 OR P(A)=1-P(A’)

Question 6

multiplication rule:

Answer 6

If A and B are independent events, then P(A and B)=P(A) x P(B)

*independent events=the occurence of one event DOES NOT affect the probability of occurence of another event

Question 7

conditional probability:

Answer 7

P(A/B)=P(A and B)/P(B) OR P(A and B)=P(A/b) x P(B)

*P(A/B) is read as: “prob. of A given B”

Question 8

combinations equation

Answer 8

C ( n!/x! (n-x)!)
n x

Question 9

probability distribution:

Answer 9

a listing of all the possible values a random variable can assume along with the probabilities of obtaining those values

can be as tables, formulas, or graphs

Question 10

for a discrete random variable x

to be a valid prob. distribution:

Answer 10

1. 0 ≤ P(x sub c) ≤ 1, for each x
2. sum of P(x)=1

Question 11

for a discrete random variable x

population mean:

Answer 11

μ=E(X)=(sum of x) x p(x)

μ= “mu”, E(x)=”expected value of x” aka long run average

basically just a weighted mean across all the possible values of x

Question 12

for a discrete random variable x

population variance=

Answer 12

sum x sqaured x p(x)-μ squared

Question 13

for a discrete random variable x

standard deviation=

Answer 13

σ=s(x)=square root 1/2

Question 14

a binomial probability distribution is

Answer 14

a common discrete probability distribution

Question 15

rules of a binomial experiment:

Answer 15

1. consists of a fixed number of trials, n
2. each trial has only 2 possible outcomes (success/failure)
3. P(success)=π ( a symbol, not actual pi)= 1-π
4. trials are independent, which means the outcome of one trial does nto affect the outcome of another trial (probability of success remains constant from trial to trial) *think: 50% of success will stay the same for heads or tails!

Question 16

the binomial random variable (x):

Answer 16

the number of successes in “n” trails. It takes on the values 0,1,2….n

x=# of successes

Question 17

to calculate the probabilities of “x” successes in “n” trials in a binomial experiment w/ probability of success, “π” use the equation:

Answer 17

p(x)=C π raised to the x (1-π) raised to
n x n-x

Question 18

for a binomial random variable:

Answer 18

μ=nπ
σ squared=nπ(1-π)
σ=square root nπ(1-π)

Question 19

normal probability distributions are:

Answer 19

-bell-shaped
-mean=median=mode
-symmetrical about the mean
-asymptotic to the x-axis (limit)
-location determined by μ and σ

Question 20

we can find probabilities for any normally distributed random variable by

Answer 20

using the standard normal distribution (aka z-distribution)

Question 21

z distribution

Answer 21

a normal distribution with μ=0 and σ=1

Question 22

standard normal random variable (z score):

Answer 22

Z= x-μ/σ

basically putting the data in standard deviation units

tells us how many standard deviations a value is from the mean

Question 23

z scores above the mean

Answer 23

will always be positive

Question 24

z scores below the mean

Answer 24

will always be negative