One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. about 24% of the canadian population over 15 years of age are first generation; that is, they were born outside canada. the number x of first-generation canadians in random samples of 1000 persons over 15 should therefore vary with the binomial (n = 1000, p = 0.24) distribution.
(a) what are the mean and standard deviation of x?

(b) use the normal approximation to find the probability that the sample will contain between 210 and 270 first-generation canadians. be sure to check that you can safely use the approximation.

Step-by-step explanation:

Given that about 24% of the Canadian population over 15 years of age are first generation; that is, they were born outside Canada.

X -  first-generation Canadians in random samples of 1000 persons over 15 should therefore vary with the binomial (n = 1000, p = 0.24) distribution.

a) Mean of X =

Var(x) =

Standard deviation =

b) When approximated to normal this variable X will be normal

we check whether np and nq are greater than 5.

Here we find both are greater than 5. So binomial to normal approximation can be done.

X is N(240, 13.51)

the probability that the sample will contain between 210 and 270 first-generation Canadians

With continuity correction this equals

true

step-by-step explanation: