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.

Question

Damon

Mathematics

6 August, 00:27

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.

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Valerie Spencer · 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