Question

A sample of 100 items is taken at random from a batch known to contain 40% defectives. What is probability that the sample contains: (i) at least 44 defectives, (ii) exactly 44 defectives?

Answer 1

Binomial problem $P=0.4,n=100P$

i. $P(\ge44)$

$P(≥44)=1−P(≤43)$

From excel Binomial formula; =BINOM.DIST(43,100,0.4,TRUE),$P(≤43)=0.763469$

Thus,

$P(≥44)=1−0.763469=0.236531$

ii. $P(=44)$

$P(=44)$ is given by =BINOM.DIST(44,100,0.4,FALSE) Excel formula, which yields 0.057629547.

Thus,

$P(=44)=0.057629547$