Question

1. The mean and standard deviation for a given data set are μ = 100 and σ = 15. By Chebyshev's Theorem, least what percentage of the data lie between 70 and 130?

2.

Suppose that you roll a die. The set of possible outcomes is S = {1,2,3,4,5,6}.

Let A = {3,4,5,6} (rolling a 3 to 6). Let B = {1,3,5} (rolling an odd number). What is P(A|B)?

3. There are 18 books along a shelf. You choose 2 at random without replacement. How many possible combinations are there if ORDER MATTERS?

Answer 1

1. The mean and standard deviation for a given data set are μ = 100 and σ = 15. By Chebyshev's Theorem, least what percentage of the data lie between 70 and 130?

By Chebyshev's Theorem, 75% percentage of the data lie between 70 and 130.

2.

Suppose that you roll a die. The set of possible outcomes is S = {1,2,3,4,5,6}.

Let A = {3,4,5,6} (rolling a 3 to 6). Let B = {1,3,5} (rolling an odd number). What is P(A|B)?

P(A|B) = P(A and B ) / P ( B ) = (2/6) / (3/6) = 2/3 = 0.6667

3. There are 18 books along a shelf. You choose 2 at random without replacement. How many possible combinations are there if ORDER MATTERS?

18P2 = 306

306 ways to choose 2 book at random