Question

1. In light of the COVID-19 situation in the US, the chance any one of the 27 Jesuit Consortium Colleges opening for fall 2020 semester with on-site student presence on campus is 15%. Father Luige Mario, who is in charge of campus readiness this year, is trying to determine how many campuses, if any, will be ready.

1. What distribution will Father Mario use to determine how many Colleges will need to be ready by fall 2020?

2. What is Father Mario’s expectation for the number of Colleges that will need to be ready by fall 2020?

3. What is the variance that Father Mario should expect?

4. What is the probability that all 27 Colleges will be open for campus activities come fall 2020?

Answer 1

(a) The Distribution used will be the Binomial Distribution as there are only 2 outcomes, opening or not opening. The number of trials are fixed and independent of each other, and the sample taken is a simple random sample.

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

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(b) Expectation = Mean = n * p = 27 * 0.15 = 4.05

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(c) Variance = n * p * (1 - p) = 27 * 0.15 * 0.85 = 3.4425

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(d) P(X = 27) = ²⁷C₂₇ * (0.15)²⁷ * (0.85)^27-27 = 0.000

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