Catherine Chao,Director of Marketing Research,needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City 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

To find the probability of the sample proportion, we use the z-test formula:
z = (p̂ - p) / sqrt((p(1-p))/n)
where:
p̂ = sample proportion = 0.45
p = population proportion = 0.4
n = sample size = 300

Substituting the values:
z = (0.45 - 0.4) / sqrt((0.4 * 0.6) / 300)
z = 2.5

Looking up the z score in a standard normal distribution table, we find the probability to be 0.0384 (rounded to four decimal places). Therefore, the correct answer is D: 0.0384.

Catherine Chao,Director of Marketing Research,needs a Sample of Kansas City