Answer Happy

a In a population of 2000 individuals 220 are left handed. (a) A sample of 200 individuals is randomly selected with replacement from this population. What is the proba- bility that exactly 10 individuals in the sample are left handed? Define an appropriate random variable and identify its distribution. Is it uniform, binomial, or ge- ometric? Briefly explain why and give the values of the corresponding parameters. (b) What is the expected number of left handed people in a random sample of 200 with replacement? (c) If individuals are selected one after the other with replace- ment, what is the probability that at most 10 individuals have to be selected to find the first left handed person? What is the expected number of individuals that have to be selected to find the first left handed person? Define an appropriate random variable and identify its distribution. Is it uniform, binomial, or geometric? Briefly explain why and give the values of the corresponding parameters. (d) A sample of 200 people is randomly selected without re- placement from this population. What is the probability that exactly 10 people in the sample are left handed? Start by defining an appropriate random variable. Ex- plain why this variable is not binomial.