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

Mathematics

Macie Gillespie

17 May, 05:46

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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Maeve Reilly · 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