A group of experimenters makes the following claim: We measured the number of co

Question

A group of experimenters makes the following claim: We measured the number of counts in 20 seconds from a radioactive source using a Geiger counter.

We repeated the measurements 100 times. We found that the average number of counts is 2859 with a standard deviation of 26. Based on what you studied in Section 2 of the lab, which statement is correct?

A)The number of counts and the standard deviation are consistent with each other according Poisson statistics. The claim is probably correct.

B)The average number of counts is inconsistent with the standard deviation according to Poisson statistics. Because the number of measurements is low, there may be clustering effects that make the experimental standard deviation unreliable. Thus, the claim is probably correct.

C)The average number of counts is inconsistent with the standard deviation according to Poisson statistics. Clustering effects should be negligible. The claim is probably incorrect.

D)The numbers presented cannot possibly be correct. The experimenters have made a mistake.

Explanation / Answer

Ans - (C)

EXPLANATION

As per Poisson distribution, mean and variance are equal. That is, mean is equal to square of standard deviation. However, by the given data, mean = 2859 and variance = 26^2 = 676.

This difference is too huge to be accounted for by clustering effects, since the number of observations is 100, i.e. not too small. Clustering effects (i.e. clusterig of observations close to the mean, leading to a small observed variance) generally disappear when number of observations are greater than 30 or 40.

Thus, the claim is probably incorrect.

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