Question

The Higher Education Research Institute at UCLA collected data from 203960 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.

71.5% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick 8 first-time, full-time freshmen from the survey. You are interested in the number of these 8 that believes that same sex-couples should have the right to legal marital status.

1. Idenitify the parameter n for the binomial experiment.

2. Identify the parameter p for the binomial experiment. Round your answer to 3 decimal places.

3. Find the probability that exactly 1 of the 8 reply that, yes, they believe that same-sex couples should have the right to legal marital status. Round your answer to 4 decimal places.

Answer 1

1) The parameter n = 8, is the sample of students picked from 203960 incoming first time, full time freshmen.

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2) The parameter p = 0.715, is the probability that an incoming first time, full time freshman would say yes, that they believed that same sex couples should have the right to legal marital status.

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(3) Please note

Binomial Probability = ⁿC_x * (p)^x * (q)^n-x, where n = number of trials and x is the number of successes.

Here n = 8, p = 0.715, q = 1 – p = .0.285

P(X = 1) = ⁸C₁ * (0.715)¹ * (0.285)^8-1 = 0.7635

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