Suppose that 20% of all subscribers to a business magazine earn an income
greater than $100,000. If the magazine takes a random sample of 20 subscribers:
(a) What is the probability that
(i) none of the 20 subscribers earn more than $100,000.
(ii) half of the 20 subscribers earn more than $100,000.
(iii) 5 or fewer of the 20 subscribers earn more than $100,000.
(b) (i) Find the expected number of subscribers in the sample who earn more than
$100,000.
(ii) Find the variance of the number of subscribers in the sample who earn more
than $100,000

thanks :) Im not very good at stats :(

Check in the Examples Section on binomial probability distributions on this site. This problem is very similar to my example.

The binomial formula will work here.

The expected value, or mean of the binomial is n*p, and the variance is n*p*q.

Ok so is this right??

a)

i) P (no subscriber earn > 100000) = P(0) = 0.0115

ii) half of subscriber earn > 100000 = P (10) = 0.0020314

iii) 5 or fewer = P(0) + P(1) + P(2) + P(3) + P(4) = 0.6296483



b) Expected no of subscriber = np = 20 * 0.2 = 4

c) Std deviation σ = √ n * p * (1-p)

So variance = (σ ^2) = n * p * (1-p) = 20 * 0.2 * 0.8 = 3.2

Thanks for all your help!

5 or fewer = P(0) + P(1) + P(2) + P(3) + P(4) = 0.6296483


Just add P(5) to your answer in a) iii) and you're all set. What you answered here was "fewer than 5."

Good job.

Brill!!! Thanks heaps ey! :D