2. Corn. Corn yield in Iowa was historically low in 2012. Yield of corn (bushels

Question

2. Corn. Corn yield in Iowa was historically low in 2012. Yield of corn (bushels per acre) in Iowa during 2012 can be described by a Normal distribution with a mean of 137 bushels per acre and a standard deviation of 15 bushels per acre. Use the 68-95-99.7 Rule (Empirical Rule) to answer the following questions.

(d) What proportion of counties have a corn yield between 122 and 182 bushels per acre? (e) 0.15% of counties have a corn yield less than or equal to what value? (f) What proportion of counties have a corn yield of at least 122 bushels per acre?

Explanation / Answer

2. Corn. Corn yield in Iowa was historically low in 2012. Yield of corn (bushels per acre) in Iowa during 2012 can be described by a Normal distribution with a mean of 137 bushels per acre and a standard deviation of 15 bushels per acre. Use the 68-95-99.7 Rule (Empirical Rule) to answer the following questions.

(d) What proportion of counties have a corn yield between 122 and 182 bushels per acre?

122=137-1*sd

182=137+3sd

P( x< mean-1sd)=0.16

P( x < mean+3sd)=P( mean-3d<x<mean+3sd)+P( x <mean-3sd)=0.9970+0.0015=0.9985

P( 122 <x <182)

=P( x <182) – P( x <122)

=0.9985-0.1600

=0.8385

(e) 0.15% of counties have a corn yield less than or equal to what value?

99.7% of values with in mean±3sd values

0.15% values below mean-3sd and 0.15% values above mean+3sd

The required value = mean-3sd

=137-3*15

=92

(f) What proportion of counties have a corn yield of at least 122 bushels per acre?

P( mean -1*sd < x < mean+1*sd)=0.68

P( x < mean-1*sd)= P( x > mean+1*sd)=0.16

P(x >122)= P( x >mean-1*sd)

P( mean -1*sd < x < mean+1*sd)+ P( x > mean+1*sd)

=0.68+0.16

= 0.84

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