Answer to Question #347256 in Statistics and Probability for Galaxy

Question

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. What is the probability that 4 of the selected students would be girls?

b. Find out the mean and standard deviation of the binomial distribution.

Answer 1

Solution: (this one last)

$N=75; N_m=55; N_ f=20;$

a) We need to find of ways for 4 girls from 20 in $^{20}C_4;$

for 6 boys from 55 in $^{55}C_6$ ways;

for 4 girls and 6 boys $^{20}C_4\times^{55}C_6$ ways;

for 10 student from 75 in $^{75}C_{10}$ ways;

$p(4)==\frac{^{20}C_4\times^{55}C_6}{^{75}C_{10}}=0.1694;$

$p(4)=16.94$ %.

b) $\mu=np=10\times0.1694=1.694$$\mu$ - mean;

$\sigma=\sqrt{npq}=\sqrt{10\times0.1694\times0.83}=1.186;$

Answer:

a) $p(4)=16.94$ %;

b) $\mu=1.694$

$\sigma=1.186.$