00:01
For this problem, to begin, we know that x is distributed as a poisson random variable with a mean value of 10.
00:07
So, well, let mu, the mean value is equal to 10.
00:12
And for a poisson random variable, we have that the variance would also be equal to 10.
00:17
Or that means that the standard deviation is equal to the square root of 10.
00:21
So our standard deviation is equal to about, one second here, it's equal to approximately 3 .16.
00:31
So the probability of x being within one standard deviation of the mean value, it's going to be equal to the probability of x being between, well, 10 minus sigma, which is going to be a value of about 6 .84, and 10 plus sigma, which would be about 13 .16.
00:58
But the prusson is discrete, so we want to really round these values to the nearest integer values...