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Probability Distributions · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SBinomial distribution and its properties6 marksPaper 2~9 min
A pharmaceutical company is testing a new vaccine. Clinical trials show that the vaccine is effective in 85%85\% of individuals who receive it. A random sample of 1212 individuals is selected from a large population. Let XX be the number of individuals in the sample for whom the vaccine is effective.
(a)
State two conditions required for XX to be modelled by a binomial distribution, referring to the context of this trial. [2 marks]
(b)
Given that X∼B(12, 0.85)X \sim B(12,\, 0.85), calculate the probability that exactly 1010 individuals find the vaccine effective. [2 marks]
(c)
The company considers the trial a concern if fewer than 99 individuals find the vaccine effective. Using your GDC, find the probability that the trial raises a concern, and hence determine whether this outcome is more or less likely than rolling a fair six-sided die and obtaining a 66. Justify your answer. [2 marks]
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