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# probability

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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?

Guest Mar 12, 2017
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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

Melody  Mar 12, 2017