The crop yield for a particular farm in a particular year is typically measured as the amount of the crop produced per acre. For example, cotton is measured in pounds per acre. It has bccn demonstrated that the normal distribution can be used to characterize crop yields over time

(Americun Journal ofAgricultura1 Economics, May 1999).

Historical data indicate that next summer's cotton yield for a particular Georgia farmer can be characterized by a normal distribution with mean 1,500 pounds per acre and standard deviation 250.The farm in question will be profitable if it produces at least 1,600 pounds per acre.

a. What is the probability that the farm will lose money next summer?

b. Assume the same normal distribution is appropriate for describing cotton yield in each of the next two summers. Also assume that the two yields are statistically independent. What is the probability that the farm will lose money for two straight ycars?

c. What is the probability that the cotton yield falls within 2 standard deviations of 1,500 pounds per acre next summer?