I am reading Probability and Statistics for Engineering and the Sciences.
Exercise 81, Chapter 3 says:
Suppose that the number of drivers who travel between a
particular origin and destination during a designated time
period has a Poisson distribution with parameter $\mu=20$
(suggested in the article “Dynamic Ride Sharing: Theory
and Practice,” J. of Transp. Engr., 1997: 308–312). What is
the probability that the number of drivers will
- Be within 2 standard deviations of the mean value?
I know that the standard deviation for a Poisson random variable has the same value of the mean (which in this case is $\mu=20$).
Therefore I computed the cumulative density function of the Poisson random variable from $0$ to $60.5$ (2 Standard deviations should be $40$).
However I get as result $0.99999999999986222$ while the correct result seems to be $0.945$. What am I missing?
Best Answer
The standard deviation is the square root of variance. The variance is $\mu$, and the standard deviation should be $\sqrt{\mu}$.