Probability and distribution ( lecture 4/11)

Question 1

5 basic propertied of the 3 types of probability

Answer 1

1. all probabilities lie between 0 and 1
2. When the outcome can never happen the probability is 0.
3. When the outcome will definitely happen the probability is 1.
4. the probability of either one of mutually exclusive events occurring is calculated using the addition rule
5. the probability of two independent events occurring is calculated using the addition rule

Question 2

the probability of any mutually exclusive event occurring are calculated using …

Answer 2

addition rule

Question 3

the probability of two independent events occurring is calculated using …

Answer 3

the multiplication rule

Question 4

In a clinical trial, death ( probability 5% ) and severe disability ( probability 25% ) are MUTUALLY EXCLUSIVE. What is the probability of either occurring.

Answer 4

25%

Mutually exclusive = addition rule

5% + 20% = 25%

Question 5

define independent events…

Answer 5

one occurring does not affect the probability of the other occurring

Question 6

give an example of independent events

Answer 6

giving birth to a boy and having a white Christmas

or

rolling 5 on one dice and 6 on another when rolling 2 die

Question 7

If we throw an equal 6-sided die, calculate the probability of throwing either five or a six.

Answer 7

cannot throw 5 and 6 at the same time - Mutually exclusive is =
(the addition rule):
P(5 or 6) = P(5) + P(6) = 1/6 + 1/6 = 2/6 or 0.333.

Question 8

Calculate the probability of throwing two 6’s when throwing 2 6-sided dice together.

Answer 8

the outcome of each die is independent of one another
therefore = independent

so multiplication rule

P(6 and 6) = P(6) x P(6) = 1/6 x 1/6 = 1/36 or 0.028.

Question 9

The standard normal distribution has a mean (meu) of… and a variance (SD= sigma) of….

Answer 9

mean = 0 
SD = 1

Question 10

The standard normal deviate is…

Answer 10

a random variable that has a standard normal distribution with a mean of zero and a SD of one

Question 11

What % of the population values in a normal distribution lies within +/- 1 SD of the mean

Answer 11

68%

Question 12

What % of the population values in a normal distribution lies within +/- 2 SD of the mean

Answer 12

95%

Question 13

What % of the population values in a normal distribution lies within +/- 3 SD of the mean

Answer 13

99.7%

Question 14

Standardised normal variate is …

Answer 14

The formula for converting any normal distribution to the standard distribution Z=(X−μ)/σ