Question

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

Answer 1

a) P=0.2861

b) P=0.0954

c) P=0.3815

d) P=0.6185

Explanation:

The question is incomplete:

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.

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

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

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

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

We use a binomial distribution with n=5, with p=10/16=0.625 (proportion of master students).

a)

`P(k=4)=\binom{5}{4}p^4q^1=5*0.625^4*0.375=5*0.1526*0.3750\\\\P(k=4)=0.2861`

b)

`P(k=5)=\binom{5}{5}p^5q^0=1*0.625^5*1=\\\\P(k=4)=0.0954`

c)

`P(k\geq4)=P(k=4)+P(k=5)=0.2861+0.0954=0.3815`

d)

`P(k\leq3)=1-P(x\geq4)=1-0.3815=0.6185`