In Thomas Pynchon's book Gravity Rainbow, the characters discuss whether the Poisson probabilistic model can be used to describe the locations that Germany's feared V-2 rocket would land in. They divided London into 0.25-km2 regions. They then counted the number of rockets that landed in each region, with the following results:

(a) Estimate the mean number of rocket hits in a region by computing µ = ΣxP(x). Round your answer to four decimal places.
(b) Explain why the requirements for conducting a goodness-of-fit test are not satisfied.
(c) After consolidating the table, we obtain the following distribution for rocket hits. Using the Poisson probability model, P(x) = µx/x! e-µ, where m is the mean from part (a), we can obtain the probability distribution for the number of rocket hits. Find the probability of 0 hits in a region. Then find the probability of 1 hit, 2 hits, 3 hits, and 4 or more hits.

(d) A total of n = 576 rockets was fired. Determine the expected number of rocket hits by computing "expected number of rockets" = np, where p is the probability of observing that particular number of hits in the region.
(e) Conduct a goodness-of-fit test for the distribution using the a = 0.05 level of significance. Do the rocket hits appear to be modeled by a Poisson random variable?

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Number of rocket hits Observed number of regions 3 4 5 35 7 0 0 229 211 93 Number of rocket hits Observed number of regions 2 3. 4 or more 211 93 35 229