Probability Distributions (8)

Question 1

What is a probability distribution

Answer 1

A list of all the possible outcomes together with their probabilities

Question 2

What is binomial distribution

Answer 2

A type of probability distribution

There can only be teo outcomes
And the probability an event occurs is (p+q)^n

Where n is the number of times

Question 3

How is binomial distribution written

Answer 3

B(n,p)

Question 4

What is needed for binomial distribution to be used

Answer 4

A fixed number of trials
Two independent trials
Only two possible outcomes (success of failure)

Question 5

How can you see the coesfficeints for binomial distribution

Answer 5

Using pascals triangle

                                1
                            1     1 
                          1    2   1
                        1   3    3  1

(Etc - 2 numbers above are added e.g 1+2 =3)

Question 6

How do you use a calculator to find the coefficient of binomila expansion

Answer 6

Use the nCr button

N is the number of trials
R is the number of outcomes you are looking for

5C2

This would mean 5 trials
And you are looking for 2 success (or failure)

Question 7

What is normal distribution

Answer 7

A bell shaped graph

Question 8

What is needed to use normal distribution

Answer 8

A symmetrical and bell shaped distribution
Continuous data
The mode median and mean are approximately equal

Question 9

How is the mean represented in normal distribution

Answer 9

It is in the centre written with the character

µ

Question 10

What percentage of observations lie between
µ +/- 1σ
µ +/- 2σ
µ +/- 3σ
µ +/- 4σ

Answer 10

µ +/- 1σ = 68%
µ +/- 2σ = 95%
µ +/- 3σ = 99.8%
µ +/- 4σ = 100%

Question 11

How is normal distribution denoted (written)

Answer 11

N(µ, σ^2)

This uses the mean and the variance (σ^2)

Question 12

If a question asks to find where ‘nearly all’ observations lie how many standard deviations should you use

Answer 12

3
(99.8%)

Question 13

What are standardized scores

Answer 13

A score calculated (e.g on a test or race) to compare with a different set

Question 14

How do you calculate standardised score

Answer 14

IF THEY ARE MODELLED BY A NORMAL DISTRIBUTION YOU CAN

(Score - mean) ÷ standard deviation

Question 15

How are standardized scores used to compare

Answer 15

The higher the standardized score the better someone did (even if their initial score is higher)

Question 16

What is quality assurance used for

Answer 16

To check samples of a product and ensure that they meet required standards

Question 17

What are control charts

Answer 17

Graphs used to show quality assurance

They can be plotted with a mean, median or range of multiple samples

The samples are plotted on the x axis

Question 18

What is a warning limit

Answer 18

A limit set so that 95% of the means of a sample fall between them

The mean is normally distributed so the warning limit is
µ +/- 2σ

Question 19

What is the action limit

Answer 19

A limit that contains 99.8% of all samples.

µ +/- 3σ

Question 20

What should a company do if a value falls between the action and warning limit

Answer 20

They should take another sample just to make sure it isnt the 5% chance

If they find multiple at these values they may have to stop production

Question 21

What should a company do if a value is outside the action limit

Answer 21

If the sample mean is outside the action limit they usually should halt the manufacturing process and restart the machinery

Question 22

Why is the target value sometimes set higher than the company actually wants

Answer 22

If their target value is higher they are more likely to reach the actual value that they eant

Question 23

How do you calculate probability of binomial distribution
E.g
B(5,3)
Chance of success = 0.30

Answer 23

1-0.30 = 0.70 = chance of failure

We need to find the coefficient so:

5C3 × (0.30)^3 × (0.70)^2

=0.1323