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14. (a) The annual number of earthquakes registering at least 2.5 on the Richter
Scale in a suburb of the USA follows a Poisson distribution with mean 6.5.
(i) (P) Find the exact probability that 12 such earthquakes will strike
next year. Round your answer to 4 decimal places.
(ii) (C/D) Using the normal approximation with continuity correction,
find the probability (close to 4 decimal places) that at least 12 such
earthquakes will strike next year.
(iii) (P) What is expected number of earthquakes within the next two
years?
(b) (HD) Suppose that a researcher wishes to estimate the mean of a popula-
tion u and to keep the error of the estimation to be less than 5 units with
probability 0.95. Find the size of the required sample given that the true
standard deviation of population is 21,

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