00:01
For this exercise, we are told that service calls occur following a poisson distribution with an average arrival rate of 70 per hour.
00:10
We are asked to use the normal approximation to the poisson to find the probability that at most 57 service calls occur in a given hour.
00:23
So let's denote the number of calls in a given hour as x.
00:28
So we want to find the probability that x is no bigger than 57, so less than or equal to 57.
00:38
Now the normal approximation to the poisson random variable is best when the average rate is greater than 20, which is the case here.
00:49
And so we can say that the number of calls is approximately normally distributed with the mean equal to the average rate and the standard deviation, the square root of the average rate.
01:11
So here we can say it's normally distributed with a mean of 70, standard deviation, square root of 70.
01:19
So to find the probability that x is at most 57, we can use software...