Question

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution
of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor
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 of the farmer will count 52 or
fewer flights on average in the next 40 rows down which he drives his tractor?
How do I arrive at the answer 0.0041?

Answer 1

sample SD = 12/sqrt(40)
z-score = (52-57)/(12/sqrt(40)) = -2.64 to 2 dp
P(z<-2.64) = 0.0041 <------