Y1, C6 - Statistical Distributions

Question 1

(Probability distributions) What does a random variable X represent

Answer 1

A single experiment / trial

Question 2

What does P(X = x) mean

Answer 2

The probability that the outcome of the random variable X was the specific outcome x

Question 3

What does it mean if you have a discrete uniform distribution

Answer 3

The probability of each outcome is the same

Question 4

If you are playing a game 15 times what is the chance of winning exactly 5 times

Answer 4

15C5
3003

Question 5

What is the formula for the binomial distribution

Answer 5

If X ~ B(n, p) then:
P(X = r) = (n, p) * p^r * (1 - p)^n-r

Question 6

When can you model a random variable X with the binomial distribution

Answer 6

When there are a number of fixed trials, n
When there are two possible outcomes, success and failure
There is a fixed probability of success, p
The trials are independent of each other

Question 7

What do p and n mean in X ~ B(n, p)

Answer 7

n = fixed number of trials
p = fixed probability of success

Question 8

How to use calculator to find cumulative probabilities
1/3 chance, 15 games, up to 6

Answer 8

Binomial CD
x = 5 (not including 6)
N = 15
p = 1/3

Question 9

How to find cumulative probability
0.25 chance, 25 games, 6 < X <= 10

Answer 9

P(M<=10) - P(M<=6)

Question 10

There are 20 exams with a probability of passing each one 0.45. You can graduate if you pass a minimum number of the 20 exams. The school wants the probability of graduating to be at least 0.1. What should the minimum number of passes be

Answer 10

X~B(20, 0.45)
P(X >= a) >= 0.9
choices of a can be written as a, a+1, a+2 …
Rearrange and sub in the missing choice (a-1)
1 - P(X <= a-1) >= 0.9
0.1 >= P(X <= a-1)
Check formula sheet table:
a = 5, therefore a = 6

OR
Try values in calculator until p >= 0.1