Question - Public Health and Nutrition Parents tend to be very good at diagnosing their children's routine medical problems, such as an ear infection, sinus infection, or strep throat. If an ailment is identified correctly, a trip to the doctor's office may be avoided. A physician may confer with a parent by telephone, and simply call a pharmacy with a prescription for an antibiotic. Suppose parents are correct 90% of the time, and 50 families with a child suffering from some minor illness are selected at random.
a. Find the mean, variance, and standard deviation of the number of parents who identify their child's illness correctly.
b. Find the probability that at least 42 parents are correct.
c. Find the probability that between 42 and 47 (inclusive) parents are correct.
d. Suppose 41 parents are actually correct. Is there any evidence to suggest that fewer than 90% of parents are correct? Justify your answer.