A farmer was interested in determining how many grasshoppers were in his field. He knows that thedistribution of grasshoppers may not be normally distributed in his field due to growing conditions. As hedrives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows hefigures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of thefarmer will count 60 or more flights on average in the next 40 rows down which he drives his tractor?
A) 0.0571
B) 0.4429
C) 0.9429
D) 0.5710

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal with mean 57 and standard deviation 12/sqrt(40). The Z-score for 60 is (60-57)/(12/sqrt(40)) = 1.58. Using the standard normal distribution table, the probability of Z being greater than 1.58 is approximately 0.0571.

A Farmer Was Interested in Determining How Many Grasshoppers Were