statistical distribution

Question 1

area under the normal distribution curve??

Answer 1

= 1

Question 2

how to find the maximum amount/ mark in a normal distribution curve

Answer 2

3 standard deviations from the mean is approximately 0.1 % of the scores
- so have to add 3 standard deviations to the mean

Question 3

standardising normal distribution curve

Answer 3

z = (x − μ) / σ

individual value - mean/ standard deviation

Question 4

what happens to the mean and standard deviation when you standardise a normal distribution curve

Answer 4

the standard deviation becomes 1

the mean becomes 0

Question 5

difference between normal and binomial distribution

Answer 5

normal distribution is for continuous data e.g. exam scores, it has symmetrical distribution and is a bell curve
and binomial distribution is NON-continuous data e.g. the height of women from a finite sample e.g. the probability of getting R result from N trials

Question 6

what does a probability distribution describe

Answer 6

• probability of any outcome in the sample space

Question 7

what is discrete distribution

Answer 7

• when all the probabilities are the same, then the distribution is known as discrete uniform distribution e.g. the score when a fair dice is rolled

Question 8

when can you model X with a binomial distribution (n, p)

Answer 8

• when there are a fixed no. of trials
• when there are only two possible outcomes (success or failure)
• when there’s a fixed probability of success
• each trial is independent

Question 9

binomial distribution formula

Answer 9

P (X= r) = ⁿCᵣ pʳ (1-p)ⁿ ⁻ʳ

Question 10

what does this cumulative probability mean:

P(X< x)

Answer 10

• gives sum of of all individual probabilities for values NOT greater than x

Question 11

what does this cumulative probability mean:

P(X ≤ x)

Answer 11

• it gives the sum of all individual probabilities for values UP TO and INCLUDING x

Question 12

what does this cumulative probability mean:

P(X ≥ x)

Answer 12

• it gives the sum of all individual probabilities for x and values GREATER than x

Question 13

what does this cumulative probability mean:

P (X > x)

Answer 13

• it gives the sum of all individual probabilities for values greater than x

Question 14

what is the normal distribution

Answer 14

• a continuous probability distribution that can be used to model many naturally occurring scenarios e.g. IQ score, height and weight

Question 15

characteristics of the normal distribution

Answer 15

• it has 2 parameters: the mean and variance
• it’s symmetrical (mean= median= mode)
• has a bell-shaped curve w/ asymptotes on each end
• total area under the curve = 1
• (P= a) = 0 for any a

Question 16

when to use the inverse normal distribution

Answer 16

• it can be used to find the value of a such that P (X >a) = p