Question

Assume 46​% of us have Group O blood. A hospital is conducting a blood drive because its supply of Group O blood is​ low, and it needs at least 124donors of Group O blood. If 279 volunteers donate​ blood, estimate the probability that the number with Group O blood is at least 124. Is the pool of 279 volunteers likely to be​ sufficient?

Answer 1

n=	279	p=	0.4600
here mean of distribution=μ=np=		128.34
and standard deviation σ=sqrt(np(1-p))=		8.3249
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

probability that the number with Group O blood is at least 124 :

probability =

P(X>123.5)

=

P(Z>-0.58)=

1-P(Z<-0.58)=

1-0.2810=

0.7190

as above probability is high but not suffiicent to conclude that at least 124 with Group O blood will be there,We require more volunteers