Question

According to a report by the Commerce Department in the fall of 2004, 20% of U.S. households had some type of high-speed Internet connection. Let Nn denote the number of U.S. households with a high-speed Internet connection in n households. What is the probability that 20 of the first 200 households surveyed have high-speed Internet given that 5 of the first 75 households surveyed have it?

Answer 1

probability that 20 of the first 200 households surveyed have high-speed Internet given that 5 of the first 75 households surveyed have it =P(15 out of next 125 have the high-speed Internet connection )

here mean of distribution=μ=np=		25
and standard deviation σ=sqrt(np(1-p))=		4.4721
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

=P(15 out of next 125 have the high-speed Internet connection )

probability =

P(14.5<X<15.5)

=

P(-2.35<Z<-2.12)=

0.0170-0.0094=

0.0076