Question

Springfield Tech is a large university. They receive thousands of applications every year and accept 18% 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

Let X is a random variable shows the number of application accepted. Here X has binomial distribution with following parameters

n= 30 and p=0.18

The probability that at least 3 of the 30 applicants are accepted is

Excel function used: "=1-BINOMDIST(2,30,0.18,TRUE)"

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The probability that at most 3 of the 30 applicants are accepted is

Excel function used: "=BINOMDIST(3,30,0.18,TRUE)"

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The probability that exactly 4 of the 30 applicants are accepted is

Excel function used: "=BINOMDIST(4,30,0.18,FALSE)"

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Using normal approximation the required probability is

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