Question

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.

1. 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

A) the population is very much larger than the sample size.

B) np > 10, and n(1-p) >10.

C) independence can be assumed, since the people were selected at random.

D) the probability of the eye examination can be assumed to be constant from person to person in the sample.

E) All of the above.

2. What is the approximate probability that the count of the number of people in the sample of size 100 who had their most recent eye examination in the previous year is more than 38?

A) 0.729

B) 0.271

C) 0.791

D) 0.209

E) Not within ± .03.

Answer 1

(1) we have p = 0.42 and n = 100

So, np = 0.42*100 = 42 and n(1-p) = 100(1-0.42) = 100*0.58 = 58

option B is correct

option A is correct because the sample size is too small as compared to the population.

option C is correct because independence as it is random selection.

option D is also correct as we can consider the probability to be constant

So, correct answer is option E "all of the above"

(2) we have n = 100, r = 38 and probability p = 0.42

using the formula 1- binomcdf(n,p,r)

setting the given values, we get

1 - binomcdf(100,0.42,38) = 1 - 0.24 = 0.760

this is close to 0.791

So, the correct answer is 0.791 option C