Population variance

In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution.

If eight students are randomly selected, find the population variance σ2 of the random variable.

If eight students are randomly selected, find the probability that three or fewer of these students will transfer to a college in the CSU system.

Correct answer:

v =  1.92
P3 =  0.1737

Step-by-step explanation:

p=60%=10060=0.6 n=8 q=1p=10.6=52=0.4  v=n p q=8 0.6 0.4=1.92
p0=(0n)p0(1p)n0=(08)0.60(10.6)800.0007 p1=(1n)p1(1p)n1=(18)0.61(10.6)810.0079 p2=(2n)p2(1p)n2=(28)0.62(10.6)820.0413 p3=(3n)p3(1p)n3=(38)0.63(10.6)830.1239  P3=p0+p1+p2+p3=0.0007+0.0079+0.0413+0.1239=0.1737



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