Questions: 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? The count of rolling an even number can be approximated with a normal distribution The count of rolling an odd number can be approximated with a normal distribution The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution Rolling an even number is considered a success

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?

The count of rolling an even number can be approximated with a normal distribution

The count of rolling an odd number can be approximated with a normal distribution

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

Rolling an even number is considered a success

Transcript text: 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? The count of rolling an even number can be approximated with a normal distribution The count of rolling an odd number can be approximated with a normal distribution The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution Rolling an even number is considered a success

Solution

Solution Steps

Step 1: Identify the probability of the outcome of interest (p)

The probability of rolling an odd number, given a fair dice, is 1/2.

Step 2: Check the conditions for the normal approximation

For the normal approximation to be valid, both np and n(1-p) should be ≥ 10. Here, np = 50 and n(1-p) = 50. Since both conditions are met, the normal approximation is considered valid.

Step 3: Evaluate the statements based on the normal approximation criteria

The statement that the count can be approximated with a normal distribution is true, and the definition of success aligns with the context.

Step 4: For statements regarding a specific sample proportion size

With a sample size of 100, the sample is sufficiently large for the normal approximation to be valid.

Final Answer:

The approximation of the distribution of outcomes to a normal distribution is valid, and rolling an even number is considered a success. The sample size of 100 is sufficiently large.

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