Final answer:
The standard deviation for the event that the odd number will be rolled 360 times is approximately 9.49.
Step-by-step explanation:
To find the standard deviation, we need to calculate the probability of rolling an odd number on a single roll of a fair six-sided die. Out of the six possible outcomes, three are odd numbers (1, 3, 5) and three are even numbers (2, 4, 6). So the probability of rolling an odd number on a single roll is 3/6 = 1/2 = 0.5
The standard deviation of a binomial distribution, such as rolling the die multiple times, can be calculated using the formula std deviation = sqrt(n * p * (1-p)), where n is the number of trials and p is the probability of success on each trial.
In this case, n = 360 (the number of times the die is rolled) and p = 0.5 (the probability of rolling an odd number). Plugging these values into the formula, we get std deviation = sqrt(360 * 0.5 * (1-0.5)) = sqrt(90) ≈ 9.49.
Therefore, the standard deviation for the event that the odd number will be rolled is approximately 9.49. Since none of the options provided match this value, none of the given options (A), (B), (C), or (D) are correct.