A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42
% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. If a sample of 100 individuals, 12 years of age or older, were selected at random from the Canadian population, we could use the Normal distribution to approximate the probability that more than 38 of the sampled people had their most recent eye examination in the previous year because the population is very much larger than the sample size.
np > 10, and n(1 – p) > 10.
independence can be assumed, since the people were selected at random.
the probability of the eye examination can be assumed to be constant from person to person in the sample.
The normal approximation is used when np>10 and n(1-p)>10.
Here, sample size=n=100 and p=0.42.
So,
np=100*0.42=42>10
n(1-p)=100(1-0.42)=100*0.58=58 >10
As, np>10 and n(1-p)>10 so, the normal distribution can be use to approximate the probability that more than 38 of the sampled people had their most recent eye examination in the previous year.
