1. STARTER P = 2A + 3B E(P) = 2 x 30 + 3 x 25 = 135
A manufacturing procedure is made up to two separate processes. The time to complete process A has mean of 30 secs and standard deviation of 3 secs. The time to complete process B has mean of 25 secs and standard deviation of 6 secs. To produce a required component (P) the manufacturer must undertake process A twice and process B three times. Assume process A is independent of process B. Find an equation linking A, B and P Find the mean and standard deviation of P
P = 2A + 3B
E(P) = 2 x x 25
= 135
var(P) = 22 x x 62
= 360
SD(P) = √360
= 18.97

2. Note 7: Binomial Distribution
Any experiment in which there are only two outcomes (success or failure) is called a Bernoulli trial.
If the process is repeated n times, and the random variable, X is the total number of successes, then X has a binomial distribution.
The conditions for X to have a binomial distribution are:
There are a fixed number of identical trials
There are only two possible outcomes for each trial
Probability of success at each trial must be constant
Each trial is independent of the other trials

3. There are two parameters n and π.
The random variable X is the total number of successes in n trials
π is the probability of success at an individual trial
The probability formula is:
Example: A duck shooter has a probability of 0.4 of hitting any duck that he shoots at during a hunt. In a hunt he fires 10 shots.

4. Explain why the duck shooter can be modelled by a binomial distribution:
There are a fixed number of identical trials
There are 10 shots
There are only two possible outcomes for each trial
Each shot – hit or miss
Probability of success at each trial must constant
Probability of hitting a duck remains constant at 0.4
Each trial is independent of the other trials
Each shot is independent of the other

5. Find the probability that he shoots exactly 8 ducks
STAT DIST BINM Bpd Var x
Numtrial 10
p 0.4
Execute
P(X = 8) =

6. Sigma
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Exercise 5.1