Question
Asked Oct 23, 2019
52 views
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?
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Expert Answer

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,

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P(X x)(P) (1-p)here x=0,1,2,..., for 0< ps1 nx

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Step 2

The required probability is,

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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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.07) (-0.070 P(X=8)= 100 |(0.000)(0.0013) 8 0.0000

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