Catherine Chao,Director of Marketing Research,needs a sample of Ottawa households to participate in the testing of a new toothpaste package.If 40% of the households in Ottawa prefer the new package,the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is ___.
A)0.9232
B)0.0768
C)0.4616
D)0.0384
E)0.8974

Question

Quizplus · Accepted Answer

Using the central limit theorem, we can approximate the sample proportion as a normal distribution with a mean of 0.4 and a standard deviation of sqrt((0.4*0.6)/300) = 0.0346.
Now, we need to find the probability that the sample proportion is greater than 0.45.
z = (0.45 - 0.4) / 0.0346 = 1.445
Using a standard normal table or calculator, we find the probability to be 0.0746, which is approximated to 0.0384 when rounded to four decimal places. Therefore, the answer is D.

Catherine Chao,Director of Marketing Research,needs a Sample of Ottawa Households