Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated children. In 2007, Bob Jones University in Greenville, SC, ended its fall semester a week early because of a whooping cough outbreak; 158 students were isolated and another 1200 given antibiotics as a precaution. Authorities react strongly to whooping cough outbreaks because the disease is so contagious. Because the effect of childhood vaccination often wears off by late adolescence, treat the Bob Jones students as if they were unvaccinated. It appears that about 1400 students were exposed. What is the probability that at least 75% of these students develop infections if not treated? (Fortunately, whooping cough is much less serious after infancy.)Is the Normal approximation permissible in this case?No, because the population is not Normal. No, because np and n(1−p) differ too much from each other. Yes, because the sample is large. No, because p is much larger than a half. Yes, because np and n(1−p) are both at least ten. Compute this probability. Use the Normal approximation if it is permissible, if not, use software to compute the exact probability. The probability isvery near to one.0.8869 .0.50 .