a. Under our assumption that the preferences of USC students are the same as those estimated by Gallup for Massachusetts, what is the exact distribution of the number of interviewed students who prefer full-time in person instruction over remote/hybrid arrangements? b. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, what is the exact probability that the number of interviewed students who prefer full-time in person instruction over remote/hybrid arrangements is (i) up to 28; and (ii) strictly less than 28? c. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, using the approximation based on the Normal distribution, what is the sampling distribution of the proportion of interviewed students who prefer full-time in person instruction?
A recent survey conducted by Gallup (an analytic and advice firm) estimated that 50% of students in Massachusetts prefer learning full-time in person, while the remaining 50% prefer a full-time remote or a hybrid arrangement. Suppose we assume that, among UCI students, the proportion of those who prefer learning full-time in person instruction is the same as that estimated by Gallup for Massachusetts. We interview a random sample of 70 USC students regarding their preferences over full-time in person versus remote/hybrid instruction.
a. Under our assumption that the preferences of USC students are the same as those estimated by Gallup for Massachusetts, what is the exact distribution of the number of interviewed students who prefer full-time in person instruction over remote/hybrid arrangements?
b. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, what is the exact
c. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, using the approximation based on the Normal distribution, what is the sampling distribution of the proportion of interviewed students who prefer full-time in person instruction?
d. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, using the approximation based on the Normal distribution that you ob- tained in part (c), (i) what is the probability that less than 28 of the 70 interviewed students declare to prefer full-time in person instruction over remote/hybrid arrangements? (ii) what is the probability that up to 28 of the 70 interviewed students declare to prefer full-time in person instruction over remote/hybrid arrangements?
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