1. ## Statistics Special Distributions

1.

A plan for an executive travelers' club has been developed by an
airline on the premise that 15% of its current customers would
qualify for membership.

a.)
Assuming the validity of this premise, among 25 randomly selected
current customers, what is the probability that exactly 2
qualify for membership?

Assuming the validity of this premise, among 25 randomly selected
current customers, what is the probability that at least 2
qualify for membership?

b.)
Again assuming the validity of the premise, what are the expected
number of customers who qualify and the standard deviation of the
number who qualify in a random sample of 25 current customers?

c.)

Let X denote the number in a random sample of 25 current customers
who qualify for membership. Consider rejecting the company's premise
in favor of the claim that more than 15% qualify if X >= 7.

What is the probability that the company's premise is rejected
when it is actually valid?

What is the probability that the company's premise is rejected
when in reality 20% qualify?

2. ## Re: Statistics Special Distributions

Hey AwesomeHedgehog.

The first thing you need to do in these kinds of questions is either choose or create a statistical model. If you have a situation of success or failure repeated n times (where they are all independent) then you have a Binomial distribution (big hint). See if you can use this information to do your questions.

3. ## Re: Statistics Special Distributions

Hey,
I got parts a and b.

For part a, I got:
b(2; 25, 15) = (25C2)*((0.15)^2)*(1-0.15)^23 = 0.161

P(X >= 2) = 1 - P(X < 2) = 1 - [P(X = 1) + P(X = 0)] = 0.906

For part b, I got:

E(X) = 25 * 0.15 = 3.75

Var(X) = 25 * 0.15 * (1 - 015) = 3.1875

sqrt(3.1875) = 1.785 = stdev

The only problem I'm having now is part c.

4. ## Re: Statistics Special Distributions

Have you studied conditional probability? (P(A|B) = P(A and B)/P(B)). If so how do you understand it? (This is a direct application of conditional probability).

5. ## Re: Statistics Special Distributions

I do not understand how that applies to part c.

6. ## Re: Statistics Special Distributions

You are looking at P(Reject Premise|Valid) and P(Reject|20% Qualify).