Question

30% of law students who sit for a bar exam pass in the first time

a. what is the probability that in a random sample of 15 law students who will sit for the bar examination at most 4 will pass in the first time

b. what is the standard deviation

Answer 1

a)

here this is binomial with parameter n=15 and p=0.3

P( at most 4 will pass in the first time ):

P(X<=4) =P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

=(15C0)*(0.30)^0*(0.7)^15+(15C1)*(0.30)^1*(0.7)^14+(15C2)*(0.30)^2*(0.7)^13+(15C3)*(0.30)^3*(0.7)^12+(15C4)*(0.30)^4*(0.7)^11

=0.0047+0.0305+0.0916+0.1700+0.2186

=0.5155

b)

standard deviation σ=√(np(1-p))=sqrt(15*0.3*(1-0.30))=1.7748