Question 182666
It is known that one out of 3 people entering a large department store will make at least one purchase. 
---
p = !/3 is therefore a population proportion
-----

If a random sample of 81 people is selected, what is the approximate probability that thirty or more of them will make at least one purchase?
-----
The distribution is binomial with p = 1/3, np = 81*(1/3) = 27, and sqrt(npq)
= sqrt(27(2/3)) = sqrt(18) = 3sqrt(2)
-------
Using the Normal Approximation:
Find the z-value of 30:
z(30) = (30-27)/[18/sqrt(81)] = 1.5
Then P(x > 30) = P(z > 1.5) = 0.067 or 6.7%
---------------------------------------------------
What is the probability that at most 40 of them will make at least one purchase?
z(40) = (40-27)/[18/sqrt(81)] = 6.5
P(x <= 40) = 1 - P(x > 40) = 1-P(z > 6.5) = 1 - 0.00000000004036 is approx "1".
=================================================
Cheers,
Stan H.