A-Level Maths | Binomial Distribution

• X~B(n, p) means that a random variable (event) X follows a binomial distribution with:
  • n - number of trials
  • p - probability of success
• P(X=x) = (ⁿC_r) x (p of success)^{no. of successes} x (p of fails)^{no. of fails)}
• Some calculators do not have an option to set a lower and upper value so you have to write the inequality using < or =

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• Hypothesis testing is usually used to check whether an outcome had a probability of less than 5%
  • If P(X..) < 0.05 then we reject our null hypothesis because we found an outlier which means our assumption of p is incorrect
  • If P(X..) > 0.05 then we do not reject our null hypothesis as the outcome is not that much of an outlier

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• Critical values are any values which would lead to a probability less than 0.05 which would lead to the null hypothesis being rejected

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• For two-tailed tests, half the significance level

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