High School

The mean yield for one-acre plots is 662 kilos with a standard deviation of 32 kilos. Assuming a normal distribution, how many one-acre plots in a batch of 1000 plots would you expect to have a yield:

(i) Over 700 kilos?
(ii) Below 650 kilos?

Answer :

Final answer:

To determine the number of one-acre plots yielding over 700 kilos and below 650 kilos, we use z-scores. Approximately 117 plots are expected to yield over 700 kilos and approximately 354 plots are expected to yield below 650 kilos.

Explanation:

To answer your question, we first need to convert our yield values to z-scores. Z-scores allow us to determine the probability of something occurring based on a normal distribution. In this case, the mean yield is 662 kilos and the standard deviation is 32 kilos.

  1. For yields over 700 kilos: we subtract the mean from 700 (700-662 = 38) and then divide by the standard deviation (38/32 = 1.1875). Using the Z-table, a z-score of 1.1875 corresponds to a probability of about 0.117. Multiply this by 1000 plots to get approximately 117 plots expected to yield over 700 kilos.
  2. For yields below 650 kilos: we subtract the mean from 650 (650-662 = -12) and then divide by the standard deviation (-12/32 = -0.375). A z-score of -0.375 corresponds to a probability of around 0.354. Multiply this by 1000 plots to get approximately 354 plots expected to yield below 650 kilos.

Learn more about Z-Scores here:

https://brainly.com/question/15016913

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