A farmer was interest in determining how many grasshoppers were in his field. He

Question

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distibution of grasshoppers may not be normally distributed in his field due to growin conditions. As he drives his tracor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability that the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor?

Explanation / Answer

Here Given Mean =57 and standard deviation = 12 , therefore variance = 144

Here n =40 rows

Though the distribution of grassshoppers not follow normal distribution , for large 'n' using Control limit therom it follows normal distribution

P(X<=52) = P[z < = (52-57)/(12/sqrt(40))] = P(z <= -2.635)=0.004

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