Consider the following results from a census in the USA givi

Consider the following results from a census in the USA, giving proportions

of the US adult population (aged 18) in various age groups.

Age Proportion 18-24 .18 25-34 .23 35-44 .16 45-64 .27

65 .16

(a) If we sample four random individuals from the US, what is the probability that one is aged between 18 and 24, one is between 35 and 44, and two are 65 or older?

(b) If we sample four random individuals and let Y1, . . . , Y5 denote the num- ber of individuals in the 5 categories, what is Cov(Y1,Y2)?

(c) If we sample four random individuals and let Y1, . . . , Y5 denote the num- ber of individuals in the 5 categories, what is Var(Y1 + Y2)?

(d) Again, we sample four random individuals. Let Z denote the total num- ber of people aged 18-34 in our sample. What is the distribution of Z?

Solution

d) it will follow a normal distribution. when a graph is made with all the probabilities if different age groups it will make a normal distribution curve and the age group 18-34 will also be a part of it.