statistics year 2

Question 1

how to prove a normal distribution can be used to model a variable

Answer 1

• state data is continous
• show majority data lies within the mean plus or minus three standard deviations
  when calculating normal distribution questions on calculator, for unkown upper/lower use plus or minus three standard deviations from the mean

Question 2

‘given’ formula

Answer 2

P(B|A) = P(A∩B)/ P(A)
P(A∩B)= P(A) x P(B|A)
this is given on the formula booklet

Question 3

standardising a score formula

Answer 3

(score-mean) /standard deviation

Question 4

equation to find z in normal distribution

Answer 4

z = (X – μ) / σ

Question 5

probability of exact number using normal distribution

Answer 5

Zero. Straight line so wont have area
-mention continous

Question 6

independent events

Answer 6

Two events, A and B, are independent if P(A|B) = P(A) or if P(A∩B) = P(A) x P(B)

Question 7

modelling with probability

Answer 7

To model real-life situations mathematically, you often have to make simplifying assumptions. You can analyse and improve your model by comparing predicted results with actual data, questioning any assumptions that have been made.
To test a binomial model you can use the mean and variance. For X- B(n,p), the mean (u) and variance σ2 are given by u=np and σ2= np(1-p)