1. We are focusing on category of tax-payer referred to as A-class, and are interested in...

1. We are focusing on category of tax-payer referred to as A-class, and are interested in simple random sample of a broader population of Ontario taxpapers (as per subquestions below). The sample size throughout is 580 tax-payers.

(a) Here we focus on an Ontario wide sample (i.e., from large population). Assume that 2.8 thousand in every 10 thousand Ontario tax-payers falls within the A-class category. Determine the probability of finding 290 or more A-class among this sample (justify any choices you make to arrive at your solution).

(b) Consider the neighborhood, Oxbrayne, with 1933 residents where 50 % fall in the A-class. Determine the probability of finding 290 or more A-class among this sample

Solutions

Expert Solution

Given :

We are focusing on category of tax-payer referred to as A-class, and are interested in simple random sample of a broader population of Ontario taxpapers.

Sample size = n = 580

a) Assume that 2.8 thousand in every 10 thousand Ontario tax-payers falls within the A-class category.

Probability = p = 2.8/10 = 0.28

Let X be number of A class tax player .

X follows the Binomial distribution with parameters n = 580 and p = 0.28

X ~ Binomial (n=580, p=0.28)

The probability density function of Binomial distribution is given by

a) The probability of finding 290 or more A-class among this sample is 0.0000

b) The the probability of finding 290 or more A-class among this sample is 0.5166

orchestra answered 1 year ago

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