Unit 2

Question 1

What is the difference between short run and long run behaviour?

Answer 1

When we observe only a small number of occurrences, the behaviour can appear random and unpredictable. When we look at the behaviour of a large number of occurrences, we start to see patterns and predictability

Question 2

What is a chance experiment?

Answer 2

Any activity or situation in which there is uncertainty about which of two or more possible outcomes occurs

Question 3

When is a variable random?

Answer 3

if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions

Question 4

What is probability?

Answer 4

the proportion of times the outcome would occur in an infinitely long series of trials

Question 5

What is the difference between proportions and probabilities?

Answer 5

proportions refer to values we have observed while probabilities refer to theoretical values after an infinite number of trials

Question 6

What is a probability distribution?

Answer 6

A mathematical model of random behaviour that consists of a list of possible outcomes and the probability of each outcome

Question 7

What is the sample space?

Answer 7

the list of possible outcomes in a probability distribution

Question 8

What are the rules of the probability model?

Answer 8

none of the probabilities will be less than zero or greater than one, and all of the probabilities will add up to one

Question 9

What is an event?

Answer 9

A subset of the outcomes in a sample space

Question 10

What is a density curve?

Answer 10

a mathematical model of a variable’s distribution. The area underneath a curve between two x-axis points represents the proportion of observations that take on values in that range (what value our variable takes on and the probability of taking on those values)

Question 11

What are the properties of density curves

Answer 11

• a density curve is always positive
• it passes the vertical line test (is a well-defined function)
• the area underneath the curve is one
• area=proportion=probability

Question 12

What is the uniform distribution?

Answer 12

probability distribution where every value is equally likely (shaped like a rectangle)

Question 13

What are parameters?

Answer 13

a number that describes an entire population

Question 14

What are statistics?

Answer 14

a number that estimates the values of parameters (computed from sample data)

Question 15

What do mu and x bar denote?

Answer 15

mu represents the population mean (parameter) and x bar represents the sample mean (statistic). We use x bar to try to estimate mu

Question 16

What do sigma and s denote?

Answer 16

sigma represents the population standard deviation (parameter) and s represents the sample standard deviation (statistic). We use s to estimate sigma

Question 17

What is the normal distribution?

Answer 17

a distribution that has values located near the middle of the distribution and they get increasingly less common as you move further away in either direction

Question 18

What is the family of normal distributions?

Answer 18

the set of all normal distributions

Question 19

What are the properties of the normal distribution?

Answer 19

• it is symmetric about mu
• single peaked
• extends infinitely far in either direction
• the curve never touches the x axis but its height gets infinitely small as X gets very large or very small

Question 20

What does changing mu do to a normal distribution graph?

Answer 20

increasing it shifts the curve to the right and decreasing shifts it to the left

Question 21

What does changing sigma do to a normal distribution graph?

Answer 21

increasing it makes the curve wider and decreasing it makes the curve narrower

Question 22

What is the empirical rule?

Answer 22

in a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7 within three

Question 23

What is the standard normal distribution>?

Answer 23

A special normal distribution with mean 0 and standard deviation 1

Question 24

What is Z a measure of?

Answer 24

how many standard deviations Z is from mu

Question 25

What do the numbers on the outside of the z table represent?

Answer 25

z scores

Question 26

What do the numbers on the inside of the z table represent?

Answer 26

proportions

Question 27

What happens if we want P(Z = b)?

Answer 27

The answer will always be zero

Question 28

What are percentiles?

Answer 28

the kth percentile is the value for which k% of observations are less than or equal to that value