4. In 2012 the Centers for Disease Control and Prevention reported that the rate of autism in children has risen to 1 in 50. A study conducted in Norway suggests that the risk of autism may be signicantly lower if women take folic acid supplements during pregnancy. Suppose a large medical center enlists 900 expectant mothers in a trial; the women agree to take the folic acid for the duration of their pregnancies. The researchers will track the children after birth to see how many deve10p autism. a) Explain why the number of autism cases is a bino- mial random variable. b) If folic acid supplements actually have no effect, what is the mean and standard deviation of the number of autism cases that these researchers might nd? c) How low would the number of autism cases among these 900 children have to be in order to convince you that the folic acid supplements may be effective? Explain your reasoning