The average number of mosquitos in a stagnant pond is 60 per square meter with a standard deviation of 16. If 25 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 62.9 mosquitos per square meter. Assume that the variable is normally distributed.
A) 0.3%
B) 18.4%
C) 31.6%
D) 81.6%

Question

Quizplus · Accepted Answer

The population mean is μ = 60 and the standard deviation is σ/√n = 16/√25 = 3.2, where n is the sample size (number of squares). 
We want to find the probability that the sample mean is more than 62.9, P(x̄ > 62.9). 
First, we need to standardize the sample mean using the formula: 
z = (x̄ - μ) / (σ/√n) = (62.9 - 60) / (3.2) = 0.91 
Using a standard normal distribution table or calculator, we can find the probability that z is greater than 0.91, which is 0.184 or 18.4%. Therefore, the probability that the average of those counts is more than 62.9 mosquitos per square meter is 18.4% or 0.184.

The Average Number of Mosquitos in a Stagnant Pond Is