A new drug that helps prevent headaches comes on the market. Tests indicate that theproportion of headache sufferers who report a benefit from taking the drug depends on thedose, and follows a normal distribution with a mean of 65 mg and a standard deviation of 6mg. However, hair loss is a possible side effect of the drug. Tests indicate that theproportion of headache sufferers who experience hair loss as a result of taking the drug alsodepends on the dose and follows a normal distribution, with a mean of 105 mg and astandard deviation of 20mg.Doses of 65, 75, 85, 95 and 105 mg are available. Which dose maximises the probabilitythat a patient receives a benefit but does not experience the side effect? What is thatprobability? What assumptions did you make to answer this question?