Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogenital warts. In a recent study based on theNational Health and Nutrition Examination Surveys (2003-2006)the prevalence of HPV was estimated for different subpopulation of females according to the various age groups.

Age Groups

HPV Prevalence (%)

14-19 32.9

20-24 53.8

25-29 46.8

30-39 44.2

40-49 42.4

50-59 38.8

Total 42.5

a.Suppose that a random sample of 12 women between the ages of 40 and 49 years were drawn from US females. What is the probability that exactly 2 of them have HPV?

b.In the same sample above (12 women between ages of 40 and 49 years), what is the probability that less than 2 of them are HPV infected?

Suppose that a sample of 200 women between age of 40 and 49 years were collected from US females, what is the probability that at most 60 of them have HPV? Write down the distribution name and the parameters. Would you be justified in approximating the probabilities using the Normal approximation? If no, explain why. If yes, explain why, and write down the mean and variance of the normal distribution you would use. (You don't need to calculate the actual probability)