Chapter 6, Problem 41E

a)

To determine

To find the weight for the 40^th percentile.

Answer to Problem 41E

The weight for the 40^th percentile is 1131.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  P(Z < z) = 0.40

  z = -0.25

Using formula,

  $x=1152+(-0.25)\times 84=1131$

Hence, the weight for the 40^th percentile is 1131.

b)

To determine

To find the weight for the 99^th percentile.

Answer to Problem 41E

The weight for the 99^th percentile is 1347.72.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  P(Z < z) = 0.99

  z = 2.33

Using formula,

  $x=1152+2.33\times 84=1347.72$

Hence, the weight for the 99^th percentile is 1347.72

c)

To determine

To find the IQR

Answer to Problem 41E

The IQR is 112.56 pounds.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $x=\mu +z\sigma$

  $IQR=Q_3-Q_1$

First, we need to find first quartile and third quartile. Therefore, we need to find z-score corresponding to a probability of 0.25 or 0.75.

  z = $\pm 0.67$

Using formula,

  $\begin{array}{l}{Q}_1=1152+(-0.67)\times 84=1095.72\\ Q_3=1152+0.67\times 84=1208.28\end{array}$

So, $IQR=1208.28-1095.72=112.56$