Question

Over the years, the percentage of candidates passing an entrance exam to a prestigious
law school is 20%. At one of the testing centers, a group of 50 candidates take the exam and 20
pass. Is this odd? Answer on the basis that probability of X ≥ 20 where X is the number that
pass in a group of 50 when the probability of a pass is 0.2.

Answer 1

n=	50	p=	0.2000
here mean of distribution=μ=np=		10
and standard deviation σ=sqrt(np(1-p))=		2.8284
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

P(X>=20)=P(Z>(19.5-10)/2.8284)=P(Z> 3.36)=1-P(Z<3.36)=1-0.9996=0.0004