GCSE Statistics Chapter 8 Summary- Probability Distributions and Quality Assurance

After completing this chapter, you will be able to;

  • Use simple cases of binominal distribution
  • Use simple cases of the discrete uniform distribution
  • Know the shape and properties of the normal distribution
  • Use the normal distribution to model distributions
  • Plot quality control charts for means and medians or ranges
  • Understand target values, and action and warning limits
  • Understand what actions need to be taken when values lie between/outside the action ad warning limits.
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Preview of GCSE Statistics Chapter 8 Summary- Probability Distributions and Quality Assurance

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Probability distributions
1.) A probability distribution is a list of all possible outcomes together with
their probabilities.
Discrete uniform distribution
2.) A discrete uniform distribution has n distinct outcomes. Each outcome is
equally likely. The probability of any given outcome = 1/n.
Binominal distributions
3.) A binominal distribution has a fixed number of independent trials n. Each
trial has only two outcomes (success and failure). The probability of success id p.
The probability of failure is q.
4.) The probabilities for the events of n binominal trials will be terms of the
expansion (p + q)^n.
Normal distribution
5.) Two properties of normal distribution are
The distribution is symmetrical about the mean
The mode, median and mean are all equal (because the distribution is
symmetrical)
6.) Further properties of a normal distribution are
95% of the observations lie within +/ two standard deviations of the
mean
Virtually all (99.8%) lie within +/ three standard deviations of the mean
7.) The variance of a normal distribution is a measure of how spread out the
data is.
Variance = standard deviation x standard deviation
Quality assurance
8.) A control chart is a time series chart that is used for process control.
9.) If a sample mean is between the warning limits the process is in control and
the product is acceptable.
10.) If a sample mean is between the warning and action limits another sample is
taken immediately to see if there might be a problem.
11.) If a sample mean is outside the action limits the process is stopped and the
machinery is reset.

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