Question

Springfield Tech is a large university. They receive thousands of applications every year and accept 16% of their applicants. A random sample of 30 applicants is selected. We are interested in the number of applicants of sample that are accepted.

1. Find the probability that at least 3 of the 30 applicants are accepted.
2. Find the probability that at most 3 of the 30 applicants are accepted.
3. Find the probability that exactly 4 of the 30 applicants are accepted.
4. Find the mean and standard deviation of the number of applicants accepted.
5. Find the probability that between 1.5 and 5.5 of the 30 applicants are accepted.

Answer 1

This is a binomial distribution question with
n = 30
p = 0.16
q = 1 - p = 0.84
where



d) Since we know that
e) P(1.5 < x < 5.5) = P(2 < x <5)
Since binomial distribuition is discrete also the number of applicant that can be accepted have to be an integer, P(1.5 < x < 5.5) = P(2 < x <5)

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