Answer to Question #253136 in Statistics and Probability for saje

Question

Smith et al. (A-5) performed a retrospective analysis of data on 782 eligible patients admitted with myocardial infarction to a 46-bed cardiac service facility. Of these patients, 248 (32 percent) reported a past myocardial infarction. Use .32 as the population proportion. Suppose 50 subjects are chosen at random from the population. What is the probability that over 40 percent would report previous myocardial infarctions?

Answer 1

The amount of subject that would report previous myocardical infractions can be described binomial distribution X = Bin(50, 0.32)

40% 0f 50 is 20.

So, we must find (P(Bin(50, 0.32) > 20). Since calculating this probability using Binomial distribution is hard and required a big amount of time, it is appropriate to use the central limit theorem and use the normal distribution.

Bin(50, 0.32) ~ N(50*0.32, 50*0.32*0.68) = N(16, 10.88) = 16 + 3.3N(0,1)

$(P(16+3.3N(0,1) > 20) = P(N(0,1) > 1.21) = 0.11314$