Exercise on Poisson distribution

[spaghetti3451]

Homework Statement

An experimenter measures the counting rate from a radioactive source as 10,150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15 percent that the number of counts recorded will be fewer than

(A) 50
(B) 70
(C) 90
(D) 100
(E) 110

Homework Equations

Poisson distribution: $P(\nu) = e^{-\mu}\frac{\mu^{\nu}}{\nu!}$, where $\mu$ is the mean and $\nu$ is the number of events for which the probability is to be calculated, both values taken over a definite interval.

The Attempt at a Solution

The first step is to find the average in 1 minute, and that is 10,150/100 = 101.50.

Now, do I have to figure out the probability for each of 101.5, 100, 99, ... , to figure out the answer, or is there an easy way?

 

[mfb]

Now, do I have to figure out the probability for each of 101.5, 100, 99, ... , to figure out the answer, or is there an easy way?

You can use the cumulative distribution.
Alternatively, make a rough estimate for the probabilities. What is the standard deviation of the count rate?
There is one correct answer, the others can be ruled out without detailed calculations.

 

[spaghetti3451]

I don't know how to calculate the standard deviation for this Poisson distribution. Could you please help me?

 

[Ray Vickson]

I don't know how to calculate the standard deviation for this Poisson distribution. Could you please help me?

Google 'Poisson distribution'.