Ph 490

February 24, 2004

Problem Set 3, due March 2, 2004

[Reference for statistics: Lab write-up "Lab B2: Radioactive Decay, Counting Statistics and the Geiger Tube," or Bevington and Robinson, Data Reduction and Error Analysis for the Physical Sciences.]

Problem 1. Suppose that, over the years, the average number of students enrolling in Ph 490 is 4. Using the Poisson distribution, calculate the probability of the number of students enrolling in a given semester being

(a) zero

(b) four

(c) more than eight

(d) Do you think that the statistical assumptions underlying the Poisson distribution are satisfied in this case? Explain.

Problem 2. Suppose that a measurement of G from a Cavendish experiment yields a value for the mass of the Earth of M_E = (7.2 ± 1.5)x10²⁴ kg. A theory of the earth postulates that it consists entirely of reinforced concrete, with a density of 2400 kg/m³. The radius of the Earth is well known to be R_E = 6380 km, and Earth's surface gravity is well known to be 9.8 m/s².

Compare experiment with theory in the "standard way." That is,

(a) Determine the discrepancy between experiment and theory.

(b) Express this discrepancy in terms of the standard deviation of the measurement; that is, give the "number of sigmas" of discrepancy.

(c) Using a table, find the probability that random errors produce a discrepancy this large or greater.

(d) From this number, give your certainty, as a percent, that the earth is not made of concrete.