Question

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 51 grams. Complete parts​ a) through​ c) below. ​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?

Answer 1

Answer:

          $\large\boxed{\large\boxed{1.33g}}$

Explanation:

Your question has one part only: 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?

Solution

You are given the mean, the reference value, and the percent of egss that exceeds that minimum.

In terms of the parameters of a normal distribution that is:

• mean = 50.1g (μ)

• X = 51 g

• Area of the graph above X = 51 g = 25%

Using a standard normal distribution 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 standard deviation (σ):

          $Z-score=(x-\mu)/\sigma$

          $0.675=(51g-50.1g)/\sigma$

          $\sigma =0.9g/0.675=1.33g$