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# Probability of Samples Containing Female Students

In a large university, 15% of the students are female. If a random sample of twenty students is selected,

a. what is the probability that the sample contains exactly four female students?

b. what is the probability that the sample will contain no female students?

c. what is the probability that the sample will contain exactly twenty female students?

d. what is the probability that the sample will contain more than nine female students?

e. what is the probability that the sample will contain fewer than five female students?

f. what is the expected number of female students?

#### Solution Preview

In a large university, 15% of the students are female. If a random sample of twenty students is selected,

a. what is the probability that the sample contains exactly four female students?

Let X be the number of female students in the sample. Then X follows a binomial distribution with n=20 and p=0.15. Then the probability that the sample contains exactly four female students is

P(X=4)=0.1821

Note: I used a Casio fx-9750 GII Calculator to find out the above probability.

b. what is the probability that the sample will contain no female students?

Let X be the number of female students in the sample. ...

#### Solution Summary

The solution determines the probability of samples containing female students.

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