STA1010 - Statistical Methods for Science - Statistics Assignment Help

Assignment Task

Question 1
A pharmaceutical research company states that a drug causes negative side effects in 2 of every 100 patients. To confirm this, another research lab identifies 6 people who have consumed the drug at a fixed dose.
a) Assuming the first lab’s statement is correct, what is the exact distribution of the number of patients who experienced side effects?
b) What is the probability that none of the six patients experience side effects? What is the probability that at least two experience side effects?
c) What is the Poisson approximation to the distribution in part a? Estimate the probabilities in part b using this approximation.
d) Comment on the differences between your answers to parts b and c.

Question 2
A new antihistamine that helps prevent seasonal allergies comes on the market. Tests indicate that the proportion of allergy sufferers who report a benefit from taking the
antihistamine depends on the dose, and follows a normal distribution with a mean of 10 mg and a standard deviation of 3 mg. However, sleepiness is a possible side effect of the new antihistamine. Tests indicate that the proportion of allergy sufferers who experience sleepiness also depends on the dose and follows a normal distribution, with a mean of 20 mg and a standard deviation of 4 mg.
Doses of 5, 10, 15, 20 and 25 mg are available. Which dose maximises the probability that a patient receives allergy relief but does not experience sleepiness? What is that probability?
What assumptions did you make to answer this question?

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