Sixty per cent of students applying for admissions at NGASCE are female. 30 applications were received on a particular day. What is the probability that exactly 15 of the applications will be from females? What is the probability that fewer than 10 of the applications will be from females? Also, calculate the expected number and variance of the number of applications from females?
+118608 Sixty per cent of students applying for admissions at NGASCE are female. 30 applications were received on a particular day. What is the probability that exactly 15 of the applications will be from females?
\(\binom{30}{15} * 0.6^{15}*0.4^{15}\approx 0.078 \)
nCr(30,15)*0.6^15*0.4^15 = 0.078312209686080141065170452
What is the probability that fewer than 10 of the applications will be from females?
nCr(30,0)*0.6^0*0.4^30+nCr(30,1)*0.6^1*0.4^29+nCr(30,2)*0.6^2*0.4^28+nCr(30,3)*0.6^3*0.4^27+nCr(30,4)*0.6^4*0.4^26+nCr(30,5)*0.6^5*0.4^25+nCr(30,6)*0.6^6*0.4^24+nCr(30,7)*0.6^7*0.4^23+nCr(30,8)*0.6^8*0.4^22+nCr(30,9)*0.6^9*0.4^21 = 0.0008563919557253
\(\text{P(less than 10 females)} \approx 0.000856\)
Also, calculate the expected number and variance of the number of applications from females?
The expected value is np = 30*0.6 = 18 females
The variance = np(1-p) = 30*0.6*0.4 = 7.2
