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Edexcel A Level Maths: Statistics:复习笔记4.4.1 Modelling with Distributions

Category: A-level课程, 国际课程, 教材笔记, 福利干货 Date: 2022年11月7日上午10:11

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

4-4-1-modelling-with-distributions-diagram-1

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.

4-4-1-modelling-with-distributions-we-solution

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.

转载自savemyexams