Supplementary Exercise 5.54 of IPS7e
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(a)
The situation is a simple random sample of size 25 from a finite 
population of size 75. The sampling is without replacement, so it is 
not a binomial setting. Furthermore, the sampled fraction of the
population is 25/75=0.3333 - so the guideline for approximation: the
sampled fraction must be no larger than 0.05, or that the population
must be at least 20 times as large as the sample, is clearly violated.


(b)
The situation is a simple random sample of size 500 from a huge
population, so that the binomial distribution is a good approximation.
Therefore, our model is a binomial B(500,p). Assuming p=0.002, the guideline
for using the normal approximation for calculations of the B(n,p) on slide
5L-7: that n*p*(1-p)>10, is clearly violated because 500*0.002*0.998=0.998. 
It may be helpful to display the binomial distribution graphically to see
why it cannot be approximated well by a normal distribution; the Minitab
command below does this (from the Probability Distribution Plot menu,
View Single, and after choosing the binomial distribution and inserting
the parameters).

MTB > DPlot;
SUBC>   Distribution;
SUBC>     Binomial 500 .002.
Distribution Plot