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At Frucht Orchards, apple trees produce an average of pounds of fruit per tree with a standard deviation of pounds. Their mango trees produce an average of pounds of fruit per tree with a standard deviation of pounds. Frucht Orchards is trying two new fertilizers. An apple tree fed Amazing Apples Fertilizer yielded pounds of fruit, while a mango tree fed Amazing Mangos Fertilizer yielded pounds of fruit. Which new fertilizer appears to be more "amazing"?

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Answer:

We can conclude that new fertilizer appears to be more effective on apple trees.

Step-by-step explanation:

Mean and standard deviation parameters are missing in the question, I will assume amounts as below:

At Frucht Orchards, apple trees produce an average of 840 pounds of fruit per tree with a standard deviation of 120 pounds. Their mango trees produce an average of 350 pounds of fruit per tree with a standard deviation of 190 pounds. Frucht Orchards is trying two new fertilizers. An apple tree fed Amazing Apples Fertilizer yielded 940 pounds of fruit, while a mango tree fed Amazing Mangos Fertilizer yielded 400 pounds of fruit. Which new fertilizer appears to be more “amazing”?  

We need to calculate standardized values (z-scores) of fertilized apple and mango trees to decide which fertilizer appears to be more "amazing".

z score for an unique value can be calculated using the equation:

z=[tex]\frac{X-M}{s}[/tex] where

  • X is the weight of the specific fruit  that the fertilized trees produce.
  • M is the average weight of the specific fruits that the trees produce.
  • s is the standard deviation of the weights of specific fruit  (583)

For fertilized apple

z=[tex]\frac{940-840}{120}[/tex]≈0.83

For fertilized mango

z=[tex]\frac{400-350}{190}[/tex]≈0.26

Since 0.83>0.26 we can conclude that new fertilizer appears to be more effective on apple trees.

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