In response to concerns about nutritional contents of fast f

In response to concerns about nutritional contents of fast foods, McDonald\'s has announced that it will use a new cooking oil for its french fries that will decrease substantially trans fatty acid levels and increase the amount of more beneficial polyunsaturated fat. The company claims that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion), what is the approximate probability that in a random sample of 1000 individuals who have purchased fries at McDonald\'s,
(a) At least 42 can taste the difference between the two oils? (Round your answer to four decimal places.)
[Incorrect: Your answer is incorrect.]

(b) At most 7% can taste the difference between the two oils? (Round your answer to four decimal places.)
[Correct: Your answer is correct.]
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

Let X be the random variable denoting the number of individuals who can detect the difference.

here number of individials is 1000. and probability that any randomly chosen individual can detect the difference is 1-97/100=0.03

so X~Bin(1000,0.03)

but since 1000 is very large and 0.03 is very small so X~Poisson(1000*0.03=30)

so pmf of X is f(x)=e^-30*30^x/x!   x=0,1,2,3,......

so a) P[X>=42]=P[X<42]=0.9779   [answer]

b) 7% of 1000 is 70

P[X<=70] is almost equal to 1   [answer]