Question

In Nebraska, the mean rain-fed corn yield of harvested fields are normally

Answer 1

Answer: 169.2 per acre are produced if a field is in the top 25%.

Step-by-step explanation:

Given:  The mean rain-fed corn yield of harvested fields are normally  distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.

Let X denote the mean rain-fed corn yield of harvested fields.

Let x denotes the number of bushels per acre are produced if a field is in the top 25%.

Top 25% on a density curve means , (100-25%)i.e. 75% area lies below x.

I.e.

$P(X$.

Z-score for p-value of 0.75 (one tailed)=0.67 [By z-table]

Then, $\dfrac{x-147.2}{33}=0.6744$

$\Rightarrow\ {x-147.2}=33\times0.67\\\\\Rightarrow\ {x-147.2}=22.11\\\\\Rightarrow\ {x}=22.11+147.2=169.31$

Here approx value is 169.2 (from options).

So, 169.2 per acre are produced if a field is in the top 25%.