BINOMIAL DISTRIBUTION A “magician” has a set of 5 sided dice (with sides marked “A, B,...

BINOMIAL DISTRIBUTION

A “magician” has a set of 5 sided dice (with sides marked “A, B, C, D, E”) that are used for tricks. The red die is a standard fair die, whereas the blue die is modified so the chances of rolling a B is 32% (and rolling A, C, D, E each have a 17% chance.)

QUESTIONS FOR PROBLEM BELOW:

1.Check that this is indeed a binomial setting, if we roll the die 10 times and are hoping for a B

2.What is the probability that exactly 2 of 10 rolls of the blue die will land on B? Show all of your work?

3.If we roll the blue die 250 times, how many times do we expect it to land on B? How many time to not land on B? What does this tell us about the Normal Approximation to the Binomial Distribution?

4.What is the value of the center and spread of the Normal Approximation to the Binomial Distribution for landing on B when we roll the blue die 250 times?

5.What is the approximate probability that when the blue die is rolled 250 times, 70 or fewer of the rolls land on B? Draw a picture with appropriate labels and scale and relevant values such as center, spread, x-value, z-score, shaded probability.

Expert Solution

orchestra answered 1 year ago

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