A new antihistamine that helps prevent seasonal allergies comes on the market. Tests indicate that the proportion of allergy sufferers who report a benet 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