Among the N=16 students taking a graduate statistics class, A=10 are master stud

Question

Among the N=16 students taking a graduate statistics class, A=10 are master students and the other N-A=6 are doctorial students. A random sample of n=5 students is going to be selected to work on a class project. Use X to denote the number of master students in the sample. Keep at least 4 decimal digits if the result has more decimal digits.

The probability that exactly 4 master students are in the sample is closest to?

The probability that all 5 students in the sample are master students is closest to?

The probability that at least 4 students in the sample are master students is closest to?

The probability that at most 3 students in the sample are master students is closest to?

Explanation / Answer

Among the N=16 students taking a graduate statistics class, A=10 are master students and the other N-A=6 are doctorial students. A random sample of n=5 students is going to be selected to work on a class project. Use X to denote the number of master students in the sample. Keep at least 4 decimal digits if the result has more decimal digits.

n=5

p=10/16 =0.625

Binomial probability used.

The probability that exactly 4 master students are in the sample is closest to?

P( x=4)= 0.2861

The probability that all 5 students in the sample are master students is closest to?

P( x=5) =0.0954

The probability that at least 4 students in the sample are master students is closest to?

P(x 4) = P( x=4)+P( x=5)

=0.2861+0.0954

= 0.3815

The probability that at most 3 students in the sample are master students is closest to?

P( x 3)

= 1- P(x 4)

= 1-0.3815

= 0.6185

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