A standard die is rolled 360 times in hopes of rolling a 5 or 6. So the probability of success is p=1/3. Find the standard deviation of the binomial distribution.
8.9
80.0
119.9
0.2
Answer is 8.9
To find the standard deviation of a binomial distribution, you can use the formula:
σ = √(n * p * (1 - p))
where σ represents the standard deviation, n represents the number of trials, and p represents the probability of success.
In this case, the number of trials (n) is given as 360 and the probability of success (p) is 1/3.
Substitute these values into the formula:
σ = √(360 * (1/3) * (1 - 1/3))
= √(360 * 1/3 * 2/3)
= √(240/9)
= √(80/3)
= √(53.33)
Now, calculating the square root:
σ ≈ 7.3
Therefore, the standard deviation of the binomial distribution is approximately 7.3.
None of the given answer options matches this result.