Question

A sample of 5 people is drawn at random from a class of 20 people, 10 of whom are smokers. Let Y be the number of smokers observed in the sample.

a. Determine the probability distribution of Y as a probability table. That is, calculate numerically p(y)=P(Y=y) for all possible value y of Y

Answer 1

The probability distribution of the number of smokers in a sample of 5 people taken from a class of 20, 10 of whom are smokers, is obtained using the hypergeometric distribution formula. The possible values of Y (number of smokers) range from 0 to 5 and the probabilities are plotted in a graph to visualize the distribution.

Step-by-step explanation:

To determine the probability distribution of the number of smokers observed in a sample (Y), we can use the hypergeometric distribution since the draws are without replacement. With a class of 20 people, where 10 are smokers, the probability P(Y=y) for y being the number of smokers in a sample of 5 is calculated given the possible values of y (which can be 0, 1, 2, 3, 4, or 5).

• Calculate the probability for each y value using the formula for hypergeometric distribution: P(Y=y) = [(Choose 10 smokers y) * (Choose 10 non-smokers 5-y)] / (Choose 20 people 5)
• List these probabilities in a table to get the probability distribution.

A graph of the probability distribution can be sketched by plotting y on the x-axis and P(Y=y) on the y-axis.