6. Statistical distributions

Question 1

What is a random variable?

Answer 1

A variable whose value depends on the outcome of a random event

Question 2

What are the three types of representing probabilities?

Answer 2

See card

Question 3

What are the conditions for the binomial distribution?

Answer 3

Fixed number of trials, n
Two possible outcomes (success or failure)
Fixed probability of success, p
Trials are independent of each other

Question 4

What is the binomial distribution? ≤≥

Answer 4

If a random variable, X, has the binomial distribution B(n, p)

Question 5

What is the cumulative probability function?

Answer 5

A cumulative probability function for a random variable X tells you the sum of all the individual probabilities up to and including the given value of x in the calculation for P(X ≤ x)
For the binomial distribution X ~ B(n, p), use the binomial CD function on the calculator

Question 6

P ( X ≤ 1 )

Answer 6

P ( X = 0 ) + P ( X = 1 )

Question 7

P ( X ≥ 15 )

Answer 7

1 - P ( X ≤ 14 )

Question 8

P ( X < 6 )

Answer 8

P ( X ≤ 5 )

Question 9

P ( X > 5 )

Answer 9

1 - P ( X ≤ 5 )

Question 10

P ( 11 ≤ X ≤ 15 )

Answer 10

P ( X ≤ 15 ) - P ( X ≤ 10 )

Question 11

P ( 10 < X < 17 )

Answer 11

P ( X ≤ 16 ) - P ( X ≤ 10 )

Question 12

P ( 15 ≤ X < 20 )

Answer 12

P ( X ≤ 19 ) - P ( X ≤ 14 )