The number of injuries per month at a certain factory has a Poisson distribution. In the past the mean was 2.1 injuries per month. New safety procedures are put in place and the management wishes to use the next 3 months to test, at the 2% significance level, whether there are now fewer injuries than before, on average.
a) Find the critical region for the test.
b) Find the probability of a Type I error.
c) During the next 3 months there are a total of 3 injuries. Carry out the test.
d) Assuming that the mean remains 2.1, calculate an estimate of the probability that there will be fewer than 20 injuries during the next 12 months.
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