Question

Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE?

a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution
b. Rolling an even number is considered a success
c. The count of rolling an even number can be approximated with a normal distribution
d. The count of rolling an odd number can be approximated with a normal distribution

Answer 1

Answer:

a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.

Step-by-step explanation:

Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.

The probability of getting an even number is $p (\text{even}) =\frac{3}{6} = \frac{1}{2}$

Since each of the rolls is independent and each probability of getting even remains the same.

Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal  distribution, it follows the Binomial distribution.

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

Answer 2

Answer:

The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.

Step-by-step explanation: