Question

2. Soybeans. Soybean yield in Iowa was historically low in 2012. Yield of soybeans (bushels per acre) in Iowa during 2012 can be described by a Normal distribution with a mean of 49 bushels per acre and a standard deviation of 7 bushels per acre. Use the 68-95-99.7 Rule (Empirical Rule) to answer the following questions. Note that answers based on the normal table rather than the empirical rule will not get any credit 99.7% of the data are within 3 standard deviations of the mean 95% within 2 standard deviations 63% within 1 standard deviation (a) Use the template above to create a well labeled normal curve for the soybean yield (bushels per acre) in Iowa during 2012. On this graph numerically label the mean (iv), the center 68% (iii) and (v), the center 95% (ii) and (vi) and the center 99.7% (i) and (vii). Report answers (i) through (vii.) in Canvas. You should also use this picture to help you answer the next few questions. db) The middle 68% of counties have a soybean yield between what two values? Cc) What is the value of the 97.5th percentile of soybean yield for counties in Iowa? ) What proportion of counties have a soybean yield between 42 and 63 bushels per acref? (e) 0.15% of counties have a soybean yield more than or equal to what value? What proportion of counties have a soybean yield of at most 35 bushels per acre?

Please answer the 4 circled questions for me.

Thank you.

Answer 1

b) Middle 68% counties have value within 1 standard deviation or (49-7,49+7) or (42,56)

c)97.5th percentile is at 2 standard devaiton to the right or (49+2*7)=63

d)42 is 1 standard deviation to the right and 63 is 2 deviations to the right. Propotion = 0.975-0.5+0.68/2=0.815

f) 35 is 2 deviations away on the left. Proportion below 2 standard deviations = 2.5%