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StatisticsQ&A LibraryThe 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?Question

Asked Oct 23, 2019

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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

will be admitted? Assume that decisions to admit are independent.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

applicants will be admitted?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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