A farmer is concerned about the number of eggs he has been collecting that are “

Question

A farmer is concerned about the number of eggs he has been collecting that are “below weight” because this impacts his profits. Hens usually begin laying eggs when they are about 6 months old. Young (6 months old to under 1 year old) hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams. The weights of the eggs are normally distributed.

If the mean weight of all the eggs produced by young hens is 50 grams, and only 25% of their eggs exceed the desired minimum weight of 54 grams, then what would the true standard deviation of the egg weights be for young hens?

Explanation / Answer

mean = 50 , x = 54 , n = 6

z value at 25% = 0.67449

z = ( x - mean) / ( s / sqrt(n))

0.67449 = ( 54 - 50) / ( s / sqrt(6))

0.67449 = 4 / (s/ 2.44949)

s = 14.526

Standard deviation = 14.526

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.