# The undergraduate admission rate at a certain university for a certain year was7​%. a. Assuming the admission rate is still77%,in a sample of100applicants to the​ university, what is the probability that exactly8will be​ admitted? Assume that decisions to admit are independent.b. What is the probability that exactly92out of100applicants will be​ rejected?a. What is the probability that exactly8out of100applicants will be​ admitted?

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The undergraduate admission rate at a certain university for a certain year was
7​%.

a. Assuming the admission rate is still
77%,
in a sample of
100
applicants to the​ university, what is the probability that exactly
8
b. What is the probability that exactly
92
out of
100
applicants will be​ rejected?
a. What is the probability that exactly
8
out of
100
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Step 1

a.

The probability that exactly 8 out of 100 applicants will be admitted is obtained below:

From the given information, admit rate is 7% that is p = 0.07, 93% are not admitted rate is (100% – 7%). The distribution is binomial distribution with sample size (n) 100 and probability of success (p) 0.07. That is, X~ Binomial (100, 0.07).

The formula for the probability of binomial distribution is,

Step 2

The required probability is,

Step 3

b.

The probability that exactly 92 out of 100 applicants will be rejected (or exactly 8 will be accepted) is obtained below:

From the given information, admit rate is 7% that is p = 0.07, 93% are not admitted rate is (100% – 7%). That is (1– p) = 0.93. The distribution is binomial distribution with sample size (n) 100 and prob...

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