Hens usually begin laying eggs when they are about 6 months old. young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams. a) young hens is 50.9 grams, and only 28% of their eggs exceed the desired minimum weight. if a normal model is appropriate, what would the standard devia- tion of the egg weights be? b) 1year, the eggs they produce average 67.1 grams, and 98% of them are above the minimum weight. what is the standard deviation for the appropriate normal model for these older hens?

a) The standard deviation of the egg's weights will be 3.37 grams.

b) The standard deviation is 4.55g.

Step-by-step explanation:

Normal model problems can be solved by the zscore formula.

On a normaly distributed set with mean \mu and standard deviation \sigma, the z-score of a value X is given by:

Each z-score value has an equivalent p-value, that represents the percentile that the value X is.

The desired minimum weight is 54 grams.

a) The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% of their eggs exceed the desired minimum weight. If a Normal model is appropriate, what would the standard devia- tion of the egg weights be?

This means that a value of is in the 100-28 = 72nd percentile.

What is the z-score of the p-value of 0.72? We have to look at the zscore table. This value is z = 0.92. This means that when . We also have that . So, we can apply the formula and find

The standard deviation of the egg's weights will be 3.37 grams.

b) By the time these hens have reached the age of 1 year, the eggs they produce average 67.1 grams, and 98% of them are above the minimum weight.

This means that a value of is in the 2nd percentile.

What zscore has a pvalue of 0.02? This is a zscore of -2.88. So, when . We also have that . So, again, we can apply the formula and find .

*(-1)

The standard deviation is 4.55g.