Question

Alice rolled a fair, six-sided die ten times and counted that she got an even number six times.

Which of the following statements is FALSE?

    The distribution of the count of getting an odd number is binomial.

    The distribution of the count of getting an even number is binomial.

    The distribution of the count of getting an even number cannot be modeled as approximately normal if the die is rolled more than 100 times.

    The distribution of the count of getting an even number can be modeled as approximately normal if the die is rolled more than 100 times.

Answer 1

When we roll a fair dice possible outcomes are 1, 2, 3, 4, 5, and 6. Out of these 6 possible outcomes, 3 are even so probability of getting a even outcome is

P(even) = 3/6 = .50

Since each roll is independent from other and each time probability of getting even remain same so it can be modeled as binomial.

If number of rolls are large then normal approximation can be used.

Correct option;

The distribution of the count of getting an even number cannot be modeled as approximately normal if the die is rolled more than 100 times.