2. Soybeans. Soybean yield in Iowa was historically low in 2012. Yield of soybea

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 68% within- 1 standard deviation

Explanation / Answer

2. (e) 99.7% lies within 3 standard deviations of mean

So, 0.3% is either above 3 standard deviations or below 3 standard deviations of mean

So, 0.15% is more than or equal to to 3 standard deviations above mean

= 49 + 3x7 = 70 bushels per acre

(f) (mean - 35)/standard deviation = (49-35)/7 = 2

So, 35 is 2 standard deviations below mean.

95% lies within 2 standard deviations

5% is above 2 standard deviation or below 2 standard deviation

Means, 5% is above 63 or below 35

Proportion of counties have a soyabean yield of at most 35 bushels per acre = 5/2 = 2.5%

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