Question

Then, answer Part B. A number cube that has sides numbered 1 through 6 is rolled 180 times. Part A How many times would you expect the result to be an even number greater than 2? Write the answer in the box. times Part B How many times would you expect the result to be a number less than 6? Write the answer in the box. times​

Answer 1

Using the binomial distribution, it is found that the expected values are given by:

a) 120.

b) 150.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem, for both items, we consider that the number cube is rolled 180 times, hence n = 180.

Item a:

4 of the 6 possible values are greater than 2, hence p = 4/6 = 2/3.

The expected value is given by:
E(X) = 180 x 2/3 = 120.

Item b:

5 of the 6 values are less than 6, hence p = 5/6.

The expected value is given by:
E(X) = 180 x 5/6 = 150.

More can be learned about the binomial distribution at brainly.com/question/24863377