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Explanation:
Your question has one part only: <em>a) The average weight of the eggs produced by the young hens is 50.1 grams, and only 25% of their eggs exceed the desired minimum weight. If a Normal model is appropriate, what would the standard deviation of the egg weights be?</em>
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<h2><em>Solution</em></h2><h2><em /></h2>You are given the <em>mean</em>, the reference value, and the <em>percent of egss that exceeds that minimum</em>.
In terms of the parameters of a normal distribution that is:
- <em>mean</em> =<em> 50.1g</em> (μ)
- X<em> = 51 g</em>
- Area of the graph above X = 51 g = <em>25%</em>
Using a standard<em> normal distribution</em> table, you can find the Z-score for which the area under the curve is greater than 25%, i.e. 0.25
The tables with two decimals for the Z-score show probability 0.2514 for Z-score of 0.67 and probabilidad 0.2483 for Z-score = 0.68.
Thus, you must interpolate. Since, (0.2514 + 0.2483)/2 ≈ 0.25, your Z-score is in the middle.
That is, Z-score = (0.67 + 0.68)/2 = 0.675.
Now use the formula for Z-score and solve for the <em>standard deviation</em> (σ):