Chapter 6, Problem 47E

a)

To determine

To find the standard deviation of younger hens.

Answer to Problem 47E

The standard deviation is 5.3448.

Explanation of Solution

Given:

  $\mu$ = 50.9

  $x$ =54

Formula:

  $z=\frac{x-\mu }{\sigma }$

From given information, if 28% exceed the desired minimum weight then 72% do not exceed the desired weight. That means, we need to find z-score corresponding to a probability of 72%.

  P(Z< z) = 0.72

  z = 0.58

Using formula,

  $\begin{array}{l}0.58=\frac{53-50.9}{\sigma }\\ \sigma =5.3448\end{array}$

b)

To determine

To find the standard deviation older hens.

Answer to Problem 47E

The standard deviation is 6.3902

Explanation of Solution

Given:

  $\mu$ = 67.1

  $x$ =54

Formula:

  $z=\frac{x-\mu }{\sigma }$

From given information, if 98% exceed the desired minimum weight than 2% do not exceed the desired weight. That means, we need to find z-score corresponding to a probability of 2%.

  P(Z< z) = 0.02

  z = -2.05

Using formula,

  $\begin{array}{l}-2.05=\frac{53-50.9}{\sigma }\\ \sigma =6.3902\end{array}$

c)

To determine

To compare younger hens with older hens.

Answer to Problem 47E

The egg sizes for the younger hens are more consistent.

Explanation of Solution

Given:

Standard deviation of younger hens = 5.3448 grams

Standard deviation of older hens = 6.3902 grams

If the standard deviation us smaller then the values are said to be more consistent. Hence, the egg sizes for the younger hens are more consistent.