Question

In: Statistics and Probability

The average number of mosquitos in a stagnant pond is 80 per square meter with astandard...

The average number of mosquitos in a stagnant pond is 80 per square meter with astandard deviation of 12. If 36 square meters are chosen at random for a mosquitocount, find the probability that the average of those counts is more than 81.6 mosquitosper square meter. Assume that the variable is normally distributed.

A)0.3%B)21.2%C)78.8%D)28.8%

Expert Solution

Solution :

Given that ,

mean = = 80

standard deviation = = 12

= / n = 12 / 36 = 2

P( > 81.6) = 1 - P( < 81.6 )

= 1 - P[( - ) / < (81.6 - 80) /2 ]

= 1 - P(z < 0.8)

= 1 - 0.7881 = 0.2119 = 21.2% , Option B is correct.

orchestra answered 3 years ago

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