Question

A farmer has found that the length of string beans he grows follows a normal distribution, having a mean of 12 cm, and a standard deviation of 1.17 cm. If the farmer can only sell beans between 9 and 15 cm long, about what percentage of the crop cannot be sold? Explain your answer.

Answer 1

μ = 12; σ = 1.17 

z = ( 9 - μ ) / σ = -2.5641 

z = ( 15 - μ ) / σ = 2.5641 

P (9 < x < 15) = P (-2.5641 < z < 2.5641) = 0.9897 = 98.97%