module 5

Question 1

random trial

Answer 1

• Any process with many possible outcomes but the result on any particular trial is unknown

Question 2

sample space

Answer 2

• set of all possible outcomes of a random trial
• typically shown within {}

Question 3

what is the outcome you are interested in called in probability

Answer 3

• event
• can be a single element in or any subset of the sample space

Question 4

random trials can have _____ or ______ variables

Answer 4

Continuous or discrete

Question 5

t or f: probabilities are formally shown as percentages

Answer 5

false, shown as proportions

Question 6

probability distributions

Answer 6

• describe probability over a range of events
• use structures of a random trial to provide compact way of describing probability of all events

Question 7

properties of a probability distribution

Answer 7

• describe the probability for the entire sample space, categorizes all possible outcomes
• area under the probability distribution always sums to one
• used to describe both cont. and discrete random variables

Question 8

area under the probability distribution always sums to _______

Answer 8

one

Question 9

discrete distributions

Answer 9

• probability distributions for discrete random variables
• whole numbers
• shown as a series of vertical bars w no spaces between, with events getting separate bars and bar area=event probability
• vertical axis=probability mass
• looks like a histogram

Question 10

vertical axis of discrete distributions are called ______

Answer 10

probability mass

Question 11

continuous distribution

Answer 11

• looks like a hill
• for continuous random variables (not whole numbers, decimals )
• shown as a single curve
• area under the curve = probability of observing and outcome in that range
• vertical axis=probability density

Question 12

vertical axis of continuous distributions are called ______

Answer 12

probability density

Question 13

if the range is 0 for continuous distributions, the probability is _____

Answer 13

0

Question 14

t or f: the probability of a single event in continuous and discrete distributions is always zero

Answer 14

false, the probability of a single event in a continuous distribution is always zero

Question 15

what can be used to answer the following questions:
what is the probability of observing an outcome over a given range of the variable?
What range of the variable is consistent with a given probability?

Answer 15

probability distributions

Question 16

standard normal distribution is a special form of the Normal distribution with mean _____ and a standard deviation of _____.

Answer 16

zero, one

Question 17

the x axis on a standard normal distribution is call the ______

Answer 17

z-score, measures the number of SDs from the mean

Question 18

what do standard normal distributions look like

Answer 18

• distributions but it is separated into slices that are one SD wide along the z-score axis

Question 19

how to convert to the standard normal distribution

Answer 19

• z=(x-μ)/σ where z=value of interest on the standard normal distribution, x= value of interest on the og distribution
• subtract the mean
• divide by the standard deviation

Question 20

The probability and range description in a problem are used to calculate a ______ from the standard Normal distribution

Answer 20

z-score

Question 21

The ______ (μ), ________(σ) and ________ (x) in a problem are used to calculate a corresponding z-score from the equation z=(x-μ)/σ.

Answer 21

mean, standard deviation, value of interest

Question 22

what are probability distributions used for

Answer 22

• calculate probability corresponding to a range of events
• calculate a range of events corresponding to a probability