Patients tend to be very good at diagnosing their children's routine medical problems; such as an ear infection, sinus infection, or strep throat infection. If an ailment is correctly identified, 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 10 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 correctly identify their child's illness.
b. Find the probability at most five parents are correct.
c. Find the probability at least six parents are correct.