Question

FOX News surveyed voters, and according to their survey results, 38% of the voters in California voted for Mitt Romney, the Republican candidate for President in 2012 (source: “Presidential election results,” http://nbcnews.com, updated Feb. 9, 2016). A small startup company in San Jose, California, has ten employees. (Hint: Find out the distribution type)

a. How many of the employees would you expect to have voted for Romney? (5 points)

b. All of the employees indicated that they voted for Obama. Determine the probability of this assuming they are representative of all California voters. (5 points)

c. Eight of the employees voted for Obama. Determine the probability that at least 8 of the employees would vote for Obama if they are representative of all California voters. (2.5 points)

d. Based on your calculations in parts b and c, do the employees reflect the California trend? Support your answer with statistical calculations and reasoning. (2.5 points)

Please provide clear explanations for the answers. Thank you.

Answer 1

ANSWER:

This is a binomial distribution question with
n = 10
p = 0.38
q = 1 - p = 0.62
where

a) Since we know that

b) x = 0 (If 10 of them voted for Obama, this means, no one voted for Romney)

c) x = 2 (If 8 or more of them voted for Obama, this means, 2 or less voted for Romney)

d)

Eventhough the probability that all the employees voted for Obama is a unusual event because the probability is less than 0.05, the probability that 8 or more of the 10 employees voted for Obama.

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