UNIT 8: Probability distributions

Question 1

Probability Distribution

Answer 1

A probability distribution is a list of all possible outcomes and their probabilities

Question 2

Binomial Distribution Notation

Answer 2

X~Bin(n,p)
n=number of trials
p= Probability of success

Question 3

Conditions for a binomial

Answer 3

• Only two outcomes - success or failure
• All trials are independent (Fixed probability of success)
• Fixed number of trials

Question 4

Mean for binomial distribution

Answer 4

n*p

Question 5

Formula for binomial

Answer 5

n^ Cr p^(n-r) q^r

n^ Cr p^r q^(n-r)

Question 6

Conditions for a Normal Distribution

Answer 6

• Continuous Data
• Symmetric distribution
• Mean =Mode=Median

Question 7

Key percentage points for normal distribution

Answer 7

• 68% of population lies within 1 standard deviation of the mean
• 95% of population lies within 2 standard deviation of the mean
• 99.8% (almost all) of the population lies within 3 standard deviation of the mean

Question 8

Notations for normal distribution

Answer 8

X~N (μ,σ^2 )
μ = mean
σ = standard deviation
σ^2 = standard variation

Question 9

Standardised Score

Answer 9

standard deviation

Question 10

Limits of standardised score

Answer 10

Usually between -3 and 3.

If it’s outside, it’s either really bad or good

Question 11

Quality assurance

Answer 11

Quality assurance involves checking samples to ensure that the product of a manufacturing process
meets the required standards.

Question 12

Sample means

Answer 12

The set of sample means will be more closely distributed than the individual values from the same population.

Question 13

Control chart

Answer 13

A control chart is a time series chart that is used for quality assurance.

Question 14

Warning limits

Answer 14

Warning limits are set so that 95% of the means of the samples should lie between them. Mean
sample mass is normally distributed, so 95% of the values lie within two standard deviations of the
mean.

Warning limits = 𝜇 ± 2σ

If a sample mean is between the warning limits the process is in control and the product is
acceptable.

Question 15

Action limits

Answer 15

Action limits are set so that all the means should lie within them.

Action limits = 𝜇 ± 3𝜎

If a sample mean is between the warning and action limits another sample is taken immediately to see if there might be a problem.

If a sample mean is outside the action limits the process is stopped and the machinery is reset.

Question 16

Range control charts

Answer 16

It is also necessary to check that the range does not vary. Ideally the range would be 0, each part produced is equal in size. In a real process there will be some variation.

Quality control charts for ranges have action and warning limits. Sometimes the lower limits are omitted.

You are not required to calculate the limits, but you must be able to use them