The survival times of adult mosquitoes exposed to a commonly used synthetic pesticide (Phenothrin) follow a gamma distribution, with a mean time until extermination of 48 sec and a standard deviation of 15.18 sec.What is the probability that a random sample of 40 mosquitoes will have an average survival time between 47.5 sec and 48 sec?
A) 0.0832
B) 0.4207
C) 0.4880
D) 0.0120

Question

Quizplus · Accepted Answer

The correct answer is A.The mean of the sample mean is equal to the mean of the population, which is 48 seconds. The standard deviation of the sample mean is equal to the standard deviation of the population divided by the square root of the sample size, which is 15.18 seconds divided by the square root of 40, which is 2.41 seconds.The probability that a random sample of 40 mosquitoes will have an average survival time between 47.5 seconds and 48 seconds is equal to the area under the normal distribution curve between those two values. The z-score for 47.5 seconds is (47.5 - 48) / 2.41 = -0.21, and the z-score for 48 seconds is (48 - 48) / 2.41 = 0.00. The area under the normal distribution curve between those two z-scores is 0.0832.

The Survival Times of Adult Mosquitoes Exposed to a Commonly