Chapter 6, Problem 39E

a)

To determine

To find the cutoff values for the highest 10% of the weights.

Answer to Problem 39E

The cutoff values for the highest 10% of the weight 1259.52

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  P(Z > z) = 0.10

  P(Z< z) = 1-0.10 = 0.90

  z = 1.28

Using formula,

  $x=1152+1.28\times 84=1259.52$

Hence, the cutoff values for the highest 10% of the weight 1259.52

b)

To determine

To find the cutoff values for the lowest20% of the weights.

Answer to Problem 39E

The cutoff values for the lowest 20% of the weight 1259.52

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  P(Z < z) = 0.20

  z = -0.84

Using formula,

  $x=1152+(-0.84)\times 84=1081.44$

Hence, the cutoff values for the lowest 20% of the weight 1081.44

c)

To determine

To find the cutoff values for the middle40% of the weights.

Answer to Problem 39E

The cutoff values for the middle 40% of the weight between 1195.68 and 1108.32.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  P(-z

  z = $\pm 0.52$

Using formula,

  $\begin{array}{l}x=1152+(-0.52)\times 84=1108.32\\ x=1152+0.52\times 84=1195.68\end{array}$

Hence, cutoff values for the middle 40% of the weight between 1195.68 and 1108.32.