The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count,
Find the probability that the average of those counts is more than 81.8 mosquitos per
Square meter. Assume that the variable is normally distributed.
A) 31.6%
B) 81.6%
C) 18.4%
D) 0.3%

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the average of those counts is more than 81.8 mosquitos per square meter. The mean of the distribution of the sample mean is equal to the population mean, which is 80 mosquitos per square meter. The standard deviation of the distribution of the sample mean (standard error) is the population standard deviation divided by the square root of the sample size, which is 12 / sqrt(36) = 12 / 6 = 2 mosquitos per square meter.To find the probability that the sample mean is more than 81.8, we calculate the Z-score for 81.8:Z = (81.8 - 80) / 2 = 1.8 / 2 = 0.9Looking up the Z-score of 0.9 in the Z-table gives us the probability of 0.8159. However, since we want the probability of being more than 81.8, we need to find the complement of this, which is 1 - 0.8159 = 0.1841 or 18.4%.

The Average Number of Mosquitos in a Stagnant Pond Is