Food protein-induced enterocolitis syndrome (FPIES) is an uncommon disorder characterized by an allergic reaction to foo

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Food protein-induced enterocolitis syndrome (FPIES) is an
uncommon disorder characterized by an allergic reaction to food
that affects the gastrointestinal system.
It is estimated that the incidence of FPIES in the USA is
0.34%.
a.) Write down the estimated incidence rate as a decimal and use
this to determine the expected number of cases of FPIES per 1000
people in the USA population.
b.) Assuming that the Poisson distribution may be used to model
X, the number of cases of FPIES diagnosed per 1000 people, find the
probabilities (correct to 4 decimal places) that in a community of
1000 people:
i. there are at most 2 diagnosed cases of FPIES;
ii. there are at least 3 diagnosed cases FPIES.
c.) Determine the mean, variance and standard deviation of
X.