Edexcel A Level Maths: Statistics:復(fù)習(xí)筆記4.4.1 Modelling with Distributions
Modelling with Distributions
When should I use a binomial distribution?
- A random variable that follows a?binomial distribution?is a?discrete random variable
- A binomial distribution is used when the random variable?counts something
- The number of successful trials
- The number of members of a sample that satisfy a criterion (satisfying the criteria can be seen as a successful trial)
- There are?four conditions?that?X?must fulfil to follow a binomial distribution
- There is a?fixed finite number of trials (n)
- The trials are?independent
- There are?exactly two outcomes?of each trial (success or failure)
- The?probability of success (p)??is constant
When should I use a normal distribution?
- A random variable that follows a?normal distribution?is a?continuous random variable
- A normal distribution is used when the random variable?measures something?and the distribution is:
- Symmetrical
- Bell-shaped
- A normal distribution can be used to model real-life data provided the?histogram?for this data is?roughly symmetrical and bell-shaped
- If the variable is normally distributed then as more data is collected the outline of the histogram should get smoother and resemble a normal distribution curve
Can the binomial distribution and the normal distribution be used in the same question?
- Some questions might require you to?first use the normal distribution?to find the?probability of success?and then use the?binomial distribution
- These questions normally involve some sort of sampling
- The key is to make sure you are very clear about what each?parameter/variable represents
Worked Example
In a population of cows, the masses of the cows can be modelled using a normal distribution with mean 550 kg and standard deviation 80 kg. A farmer classifies cows as?beefy?if they weigh more than 700 kg. The farmer takes a random sample of 10 cows and weighs them.
Find the probability that at most one cow is?beefy.
Exam Tip
- Always state what your variables and parameters represent.? Make sure you know the conditions for when each distribution is (or is not) a suitable model.
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