Patients tend to be very good at diagnosing children's routine medical problems; like ear infection, sinus infection, or strep throat infection. If ailment is correctly identified, trip to doctor's office may be avoided. Physician may confer with parent by telephone, and simply call pharmacy with prescription for antibiotic. Assume parents are correct 90% of time and 10 families with child suffering from some minor illness are selected at random.
Compute mean, variance, and standard deviation of number of parents who correctly recognize their child's illness.
Determine the probability at most five parents are correct.
Determine the probability at least six parents are correct.