Question

What type of shopping websites do males aged 18 to 34 visit? About 50% of male Internet users in this age group visit an auction site (such as eBay) at least once a month.

(a) If we interview a random sample of 14 male Internet users aged 18 to 34, what is the probability that exactly 11 of the 14 have visited an auction site in the past month? (Round your answer to four decimal places.)

b) Suppose that we had interviewed a random sample of 900 men aged 18 to 34. What is the probability that at least 435 of the men in the sample visit an online auction site at least once a month? (Round your answer to four decimal places.)

Answer 1

a)

here this is binomial with parameter n=14 and p=0.5

probability that exactly 11 of the 14 have visited an auction site in the past month:

P(X=11)=

(14C11)0.511(1−0.5)(14-11)    =

0.0222

b)

here mean of distribution=μ=np=		450.00
and standard deviation σ=sqrt(np(1-p))=		15.00
for normal distribution z score =(X-μ)/σx

  

therefore from normal approximation of binomial distribution and continuity correction:

probability that at least 435 of the men in the sample visit an online auction site at least once a month:

probability =P(X>434.5)=P(Z>(434.5-450)/15)=P(Z>-1.03)=1-P(Z<-1.03)=1-0.1515=0.8485