3.38 Left-handed.. Studies suggest that approximately 10% of the world populatio

Question

3.38 Left-handed.. Studies suggest that approximately 10% of the world population is left- handed. Use ten simulations to answer each of the following questions. For each question, describe your simulation scheme clearly. (a) What is the probability that at least one out of cight people are left-handed? b) On average, how many people would you have to sample until the first person who is left- handed? (c) On average, how many left-handed people would you expect to find among a random sampl of six people?

Explanation / Answer

(a) We get 10 simulations from Binom(8,0.1) and take the proportion of time the variable was more than 1. The code is:

left_1 = mean(rbinom(10,8,0.1) > 1)

(b) The number of people before the first person is left-handed follows geom(0.1), we have 10 simulations by the following code

left_2 = mean(rgeom(10,0.1)+1)

(c) we simulate bin(6,0.1) 10 times. We take the mean to find the average. The code is following

left_3 = mean (rbinom(10,6,0.1))

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