Probability Distributions

Question 1

What shape does a graph of a normal distribution have

Answer 1

a “bell shape”

Question 2

what are the parameters of the normal distribution

Answer 2

the mean and standard deviation

Question 3

in a normal distribution, approximately ____ of the values lie between one standard deviation below the mean and one standard deviation above the mean

Answer 3

68%

Question 4

in a normal distribution, approximately ____ of the values lie between two standard deviations below the mean and two standard deviations above the mean

Answer 4

95%

Question 5

in a normal distribution, approximately ____ of the values lie between three standard deviations below the mean and three standard deviations above the mean

Answer 5

99%

Question 6

The total area under a normal distribution curve is?

Answer 6

1

Question 7

when is a continuity correction required

Answer 7

when normal distributions are used to approximate situations that are actually discrete, for example, when measurements are rounded

Question 8

how do you do a continuity correction

Answer 8

for example, if something is measured to the nearest centimetre, it could be half a centimetre below the value in order to be counted as that value, so you put the value half a centimetre below the value into your calculator to get your answer

Question 9

what is an inverse normal distribution

Answer 9

when we are given a probability and need to work backwards to find an x value (or the mean or standard deviation)

Question 10

is a triangular distribution continuous or discrete

Answer 10

continuous

Question 11

what are the parameters of the triangular distribution

Answer 11

a = minimum 
b = maximum
c = mode (most likely value or peak)

Question 12

in a triangular distribution, which feature of the graph shows the probability

Answer 12

area under the function (triangle)

Question 13

what is the height of the peak of a triangular distribution

Answer 13

2/b-a

Question 14

which part of the formula do you use to find the height of a point on the triangle on the left side

Answer 14

top one

Question 15

which part of the formula do you use to find the height of a point on the triangle on the right side

Answer 15

bottom one

Question 16

what is the formula for the area of a triangle

Answer 16

0.5 x base x height

Question 17

is the uniform distribution continuous or discrete

Answer 17

continuous

Question 18

what shape is the uniform distribution

Answer 18

rectangle

Question 19

in what situations is the uniform model used

Answer 19

where outcomes are expected to occur within a particular range of values and each value within the range is equally likely to occur

Question 20

what are the parameters of the uniform distribution

Answer 20

a = minimum
b = maximum

Question 21

what feature of the uniform distribution shows the probability

Answer 21

area under the function

Question 22

what formula can be used to find the height of the rectangle for the uniform distribution

Answer 22

1/b-a

Question 23

what is the approach we use for an inverse question for both triangular and uniform distributions

Answer 23

to form and solve an algebraic expression by setting the area formula equal to the known probability

Question 24

for an inverse triangular distribution question, what form do you want to get the algebraic expression into?

Answer 24

a quadratic equation on the top of the fraction for the height, make this a quadratic equation equal to 0, then you will be able to use your calculator to solve it and discard a value that isn’t possible

Question 25

what are the models for continuous distributions

Answer 25

normal, triangle, uniform

Question 26

what do we call just a regular 'discrete' distribution

Answer 26

the table thingy with values for x and the probabilities for these

Question 27

how do you work out a mean E(x) of a regular 'discrete' distribution

Answer 27

multiply and add multiply the x value by the probability of everything in the table and add them all together

Question 28

how do you find the variance of a regular 'discrete' distribution

Answer 28

square the x values, then multiply these by the original probabilities and add these all together then minus the mean squared to get the variance

Question 29

how do you get the standard deviation of a regular 'discrete' distribution

Answer 29

square root of the variance

Question 30

expected value is also known as?

Answer 30

the mean

Question 31

the notation for expected value is?

Answer 31

E[x]

Question 32

what is the notation for variance

Answer 32

Var[x]

Question 33

true or false, VAR[X-Y] = VAR[X]+VAR[Y]

Answer 33

true, always add variances

Question 34

when is the binomial distribution used

Answer 34

when calculating the probability of a certain number of 'successes' out of a fixed number of trials

Question 35

what are the conditions of the binomial distribution

Answer 35

1. the number of trials must be fixed 2. there are only two possible outcomes for each trial ('success' and 'failure') 3. the probability of success at each trial must be the same 4. each trial must be independent of the others

Question 36

what are the parameters of the binomial distribution

Answer 36

n (numtrial) represents the number of trials conduted p is the probability of success for each trial

Question 37

how do you primarily solve binomial and poisson problems

Answer 37

in your calculator: stat dist binm or poiss ppd or pcd or bcd or bpd.

Question 38

is binomial discrete or continuous

Answer 38

discrete

Question 39

is poisson discrete and continuous

Answer 39

discrete

Question 40

when do you use a poisson distribution

Answer 40

represents the number of times an event occurs in a specific length of time or amount of space

Question 41

what are the conditions of the poisson distribution

Answer 41

1. events cannot occur simultaneously 2. each occurrence is independent of the other occurrences 3. events occur at random, and are unpredictable 4. for a small interval, the probability of the event occurring is proportional to the size of the interval

Question 42

what is the parameters of the poisson distribution

Answer 42

λ - the mean number of times the event occurs in a particular interval

Question 43

in a graph of a discrete distribution, what feature represents the probabilities of each value

Answer 43

the heights of the bars