8 Probability Distributions

Question 1

probability distribution

Answer 1

set of possible outcomes together with their probabilities

Question 2

notation for a binomial distribution (+ mean)

Answer 2

B(n,p)

Binomial
no. trials
probabilty of success

mean is np

Question 3

conditions for a binomial distribution

Answer 3

fixed no. trials
trials are independent
there are only two possible outcomes - success (p) and failure (q)

Question 4

using calculator for binomial distribution

Answer 4

coefficients (no. ways to get the desired outcome) can be found using:
[no. trials] nCr [no. successes]

Question 5

pattern of coefficients of a binomial distribution

Answer 5

pascal’s triangle

Question 6

notation for a normal distribution (and how do they affect the shape)

Answer 6

N(μ, σ²)

Normal
μean
σ² (variance - measure of how spread out the data is)

μ determines the centre of the normal distribution, while σ² controls its spread (greater σ² = higher width = lower peak)

Question 7

conditions for a normal distribution

Answer 7

continuous data
symmetrical/non-skewed + bell shaped distribution
mode = median = mean (approx.)

Question 8

3 important properties of a normal distribution

Answer 8

(in each case half the area lies either side of the mean - symmetry)

Question 9

standarised scores (definition, formula, purpose)

Answer 9

are the number of standard deviations above or below the mean that the data value lies
- also called z scores

z = (x - μ) / σ
standardised score = (score - mean) / standard deviation

• used to compare 2 normally distributed data sets

Question 10

interpreting z scores

Answer 10

if a score is greater than the mean, z is positive
if a score is less than the mean. z is negative

Bill does better than Bob, because he got the higher (most of the time) standardised score

Question 11

quality assurance

Answer 11

checking samples to ensure the product of a manufacturing process meets the required standards

Question 12

sample means VS individual values (from the same population)

Answer 12

Question 13

control charts (what are they, what are they used for)

Answer 13

Question 14

interpreting control charts (warning limits & action limits)

Answer 14

WARNING LIMITS:
set at μ ± 2σ (usually)
- 95% lie between them - these are acceptable
- 1 in 20 lie outside them - another sample is taken if this is the case (between warning and action limits - 4.8%) to see if there is a problem

ACTION LIMITS:
set at μ ± 3σ (usually)
- 99.8% lie between them
- 0.2% lie outside them - the process is stopped and the machine is reset in this case

Question 15

control charts can be constructed to show the _______________ of samples.

In most manufacturing processes, the _________ will be used

Answer 15

mean,median,range

mean and range