5. It is now generally accepted that cigarette smoking causes heart disease, lung cancer, and many other dis- eases. However, in the 1950s, this idea was controversial. There was a strong association between smoking and ill-health, but association is not causation. R. A Fisher advanced the \"constitutional hypothesis: \" there is some genetic factor that disposes you both to smoke and to die. To refute Fisher's idea, the epidemiologists used twin studies. They identified sets of smoking-discordant monozygotic twin pairs. \"Monozygotic\" twins come from one egg and have identical genetic makeup; \"smoking-discordan \" means that one twin smokes, the other does not. The researchers collected data on which twin dies rst, the smoker or the non-smoker. The data from a Finnish twin study are shown in the following table. Smokers Non-smokers All Causes 17 5 Coronary heart disease 9 0 Lung Cancer 2 0 According to the rst line of the table, there were 22 smoking-discordant monozygotic twin pairs where at least one twin of the pair died. In 17 cases, the smoker died rst; in 5 cases, the non-smoker died rst. According to the second line, there were 9 pairs where at least one twin died of coronary heart disease; in all 9 cases, the smoker died rst. According to the last line, there were 2 pairs where at least one twin died of lung cancer, and in both pairs the smoker died first. For parts (a)-(c) suppose that each twin in the pair is equally likely to die rst, regardless smoking or not. So the number of pairs in which the smoker dies rst is like the number of heads in coin-tossing. (a) Under this assumption, what is the chance of having 17 or more pairs out of 22 where the smoker dies rst? Calculate this probability using the Binomial formula. (b) Calculate the probability in (a) using normal approximation with continuity correction. Compare your answer with that in (a). (c) Using the Binomial formula, calculate the chance that, the smokers die rst in all of the 9 pairs from coronary heart disease. ((1) Can you use the normal approximation to calculate the probability in (c)? Why or why not? (e) Can the difference between the death rates for smoking and non-smoking twins be explained by chance? genetics? or heath effects of smoking? Explain your reasoning