Question

Suppose voters from a simple random sample of 500 (N > 1,000,000) are interviewed and asked which presidential candidate they're going to vote for. Of these, 35% say they'll vote for the Statistics Party. You want to know the probability, assuming this proportion is correct for the population, that more than 40% of a random sample of 500 people will vote for the Statistics Party. Which of these shows the three ways you could find your answer?

A. A-Using the Central Limit Theorem: 1 - binomcdf(500,.35,200) A-As a sampling distribution: normalcdf(200,E99,175,10.66) A-As a sampling distribution: normalcdf(199,E99,175,10.66) B. B-Proportion, using a normal approximation: normalcdf(200,E99,175,10.66) B-Exact binomial count: normalcdf(.40,E99,.35,.0213) B-Binomial count, using normal approximation: normalcdf(200,E99,175,10.66) C. C-Proportion, using normal approximation: normalcdf(.40,E99,.35,.0213) C-Exact binomial count: 1 - binomcdf(500,.35,200) C-Binomial count, using normal approximation: normalcdf(200,E99,175,10.66) D. D-Using the Central Limit Theorem: 1 - binomcdf(500,.35,200) D-As a sampling distribution: 1 - binomcdf(500,.40,200) D-Using the Central Limit Theorem: 1 - binomcdf(500,.35,199) E. E-Proportion, using a normal approximation: 1 - binomcdf(500,.35,200) E-Exact binomial count: normalcdf(.40,E99,.35,.0213) E-Binomial count, using normal approximation: normalcdf(200,E99,175,10.66)

Answer 1

Here we have

p = 0.35, n=500

The sampling distribution of sample proportion will be approximately normal with mean

l p 0.35

and standard deviation

p(1 -p) 0.35 0.65 0.0213 = 500

Correct option is:

C-Proportion, using normal approximation: normalcdf(.40,E99,.35,.0213)