A new drug that helps prevent acne comes on the market. Tests indicate that the proportion of acne sufferers who report a benefit from taking the drug depends on the dose, and follows a normal distribution with a mean of 30 mg and a standard deviation of 3 mg. However, headaches are a possible side effect of the drug. Tests indicate that the proportion of acne sufferers who experience headaches as a result of taking the drug also depends on the dose and follows a normal distribution, with a mean of 50 mg and a standard deviation of 10mg. Doses of 30, 35, 40, 45 and 50 mg are available. Which dose maximises the probability that a patient receives a benefit but does not experience the side effect? What is that probability? What assumptions did you make to answer this question?