Stats GCSE Probability Distributions

What is a probability distribution?

A list of all the possible outcomes together with their probabilities

What are the conditions for BD?

There’s fixed number of trials

Each trial has 2 outcomes

All the trials are independent of each other

Probabilities are fixed

What do p&q stand for in BD?

p-probability of success

q-probability of failure

How to find probabilities in BD

Identify the 2 outcomes and find their probabilities

Expand (p+q)^n, leaving p and q as letters

Find the terms that has p to the power of x successes

Substitute values of p and q, then calculate

How to show BD

B(n,p)

What’s the mean of BD?

np (number of trials\*probability of success)

Calculator shortcut for BD

Find the coefficient by using nCr (n is trials and r is successes)

How to show ND

N(μ,σ^2)

What does μ and σ^2 stand for in ND?

μ-mean

σ^2- variance

What does ND look like?

Smooth bell shaped curve

What are the conditions for ND

the data is continuous

the distribution is symmetrical

the mode, median, and mean are about the same

What kind of data works for ND?

Heights, weights, time

What is ND not suitable for?

Skewed data

What percentage of the data lies within 1sd of the mean?

68%

What percentage of the data lies between 2sd of the mean?

95%

What percentage of the data lies within 3sd of the mean?

99\.8%

What are standardised scores used for?

Comparing how far above or below average individual values are

How to calculate standardised score

(score-mean)/standard deviation

How to interpret standardised score

positive-score>mean

negative-score

What is quality assurance?

Checking samples to make sure products are of good quality

What is a control chart?

Time series chart used for quality assurance

What are the 5 lines on a control chart for?

middle line-target value

inner two lines-upper and lower warning limits

outer two lines-upper and lower action limits

What are the warning limits on a control chart?

2sd above/below target value

What do you do if a sample is outside the warning limits?

Take another sample to see if there is a problem, and if so production is stopped

What are the action limits on a control chart?

3sd above/below target value

What do you do is a sample is outside action limits?

Stop production immediately