Yes, this situation can be considered a Bernoulli trial, as each roll of the die is independent and has a fixed probability of success (rolling a 5).
To calculate the variance of the number of times a 5 is rolled in 20 rolls, we can use the formula for the variance of a Bernoulli distribution:
Variance = np(1-p)
where n is the number of trials (20) and p is the probability of success (1/6, since there is 1 success out of 6 possible outcomes on a fair die).
Variance = 20 * (1/6) * (5/6) = 1.389
To calculate the standard deviation, we simply take the square root of the variance:
Standard deviation = sqrt(1.389) ≈ 1.179
Therefore, the variance of the number of times a 5 is rolled in 20 rolls is 1.389 and the standard deviation is approximately 1.179.
a fair die is rolled 20 times each time a 5 is rolled is recoreded is this a bernouli tira
calcuate the variance and standard deviation
1 answer
1 answer