Question

The average number of mosquitoes in a stagnant pond is 70 per square meter with a standard deviation of 8 per square meter. if one square meter of the pond is chosen at random for a mosquito count, find the probability that the average of the count is more than 68 mosquitoes per square meter. assume that the variable is normally distributed.

Answer 1

the probability that the average of the count is more than 68 mosquitoes per square meter. assuming that the variable is normally distributed will be calculated as follows:
z=(x-μ)/σ
where:
x=68
μ=70
σ=8
thus
z=(68-70)/8=-0.25

P(x>68)=1-P(x<68)=1-P(z<-0.25)
=1-0.4013
=0.5987

Answer: P(x>68)=0.5987