Question

. In Southern California, a growing number of individuals
pursuing teaching credentials are choosing paid internships over
traditional student teaching programs. A group of eight candidates
for three local teaching positions consisted of **five who
had enrolled in paid internships** and **three who
enrolled in traditional student teaching programs.** All
eight candidates appear to be equally qualified, so three are
randomly selected to fill the open positions. Let Y be the number
of internship-trained candidates who are hired.

(a) Find the probability that two or more internship-trained candidates are selected to be hired. (there are 5 internship trained candidates and 3 traditional student teaching candidates)

(b) Find the mean and variance of Y

Answer #1

A group of eight candidates for three local teaching positions consisted of five who had enrolled in paid internships and three who enrolled in traditional student teaching programs.

Thus probability of selecting a candidate who had enrolled in paid internships = 5/8 = 0.625

3 candidates are randomly selected.

Let Y be the number of internship-trained candidates who are hired.

Thus clearly, Y ~ Binomial(3,0.625)

Thus the probability that two or more internship-trained candidates are selected to be hired

Y ~ Binomial(3,0.625)

Thus mean of Y = 30.625 = 1.875

Thus variance of Y = 30.625(1-0.625) = 0.703125

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