S2- Binomial Distribution

Question 1

P(X=x) =

Answer 1

(nCx)(p^x)(q^(n-x))

Question 2

When don’t you need to use the full formula for P(X=x)?

Answer 2

1. 0 success: (1-p)^n

2. n successes: P^n

Question 3

Assumptions for binomial distribution

Answer 3

1. fixed number of trials
2. probability of success is constant
3. each trial is independent
4. each trial is either success or failure

Question 4

E(X) for binomial

Answer 4

np

Question 5

Var(X) for binomial

Answer 5

npq (q=1-p)

Question 6

When would you switch from number of successes to number of failures?

Answer 6

To get the probability to be less than 0.5, in order to use the tables

Question 7

How does the probability change when going from number of successes to number of failures?

Answer 7

p goes to (1-p)

Question 8

What else changes when you switch from successes to failures?

Answer 8

1. The inequality gets flipped

2. k number of successes goes to n-k number of failures

Question 9

How is the Binomial Distribution described?

Answer 9

X~ B(n,p)

Question 10

Why is it important to specify ‘large number of …’ in a question?

Answer 10

The probability of success varies by such a small amount without replacement.