6.51 Binomial assumptions For the following random variables, check whether the conditions needed to use the binomial distribution are satisfied or not. Explain

a. X = number of people suffering from a contagious disease in a family of 4, when the probability of catching this disease is 2% in the whole population (binomial, n = 4, p = 0.02). (Hint: Is the independence assumption plausible?)

b. X = number of unmarried women in a sample of 100 females randomly selected from a large population where 40% of women in the population are unmarried

(binomial, n = 100, p = 0.40).

c. X = number of students who use an iPhone in a random sample of five students from a class of size 20, when half the students use iPhones (binomial, n = 5, p = 0.50).

d. X = number of days in a week you go out for dinner.