Answer to Question #104675 in Statistics and Probability for ps

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

It is a Binomial problem with$P=0.4, n=100$

i. $P(\ge44)$

$P(\ge44)=1- P(\le43)$

From excel Binomial formula; =BINOM.DIST(43,100,0.4,TRUE),$P(\le43)=0.763469$

Thus, $P(\ge44)=1-0.763469=0.236531$

ii. $P(=44)$

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

Thus,

$P(=44)= 0.057629547$