Question

7. Suppose that 8% of all people that experience a heart attack will die during hospitalization. (a) Consider a random sample of 30 people who experienced a heart attack. What is the probability that exactly four of them will die during hospitalization? To answer this question, first define an appropriate random variable X. Identify the probability distribution of X including the parameter values. (b) Is the probability distribution you used in part (a) the true probability distribution of X? If not, is your answer in part (a) still approximately correct? Explain.

Answer 1

Solution:

Given that Suppose that 89. of all people that experience a heart attack will die during hospitalization. forca): * A Random sample of 30 people is taken. * Let x bea random variable denoting the No of people who die during hospitalization from a heart attack. * 50 x follows binomial distribution with Parameters n- 3o an 4 - 0 0 8 : e xo Bin C30, 0-08) * The probability that exactly 4of them will die during hospitalization will be Where tomp ud => e24 (2.434 4! P(x - 4), aº caº do 30x0.08 1 = 2:4 => 0.12541 so the probability -0.12541 for cbji * The probability distribution used in part ca) to find the probabilily is popgjon distribution.

good * This is because when n is Large and pis small and when np<5, Poisson distribution is a approximation to the binomial distribution * the true distribution of x is binomial.