Chapter 6, Problem 37E

a)

To determine

To find the percent of steers weigh over 1250.

Answer to Problem 37E

The 12.17% of steers weigh over 1250.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $z=\frac{1250-1152}{84}=1.1667$

  $\begin{array}{l}P(Z>1.1667)=1-P(Z<1.1667)\\ P(Z>1.1667)=1-0.8783=0.1217\end{array}$

Hence, the 12.17% of steers weigh over 1250.

b)

To determine

To find the percent of steers weigh under 1200 pounds.

Answer to Problem 37E

The 71.61% of steers weigh under 1200 pounds.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $z=\frac{1200-1152}{84}=0.5714$

  $P(Z<0.5714)=0.7161$

Hence, the 71.61% of steers weigh under 1200 pounds.

c)

To determine

To find the percent of steers weigh between 1000 and 1100 pounds.

Answer to Problem 37E

The 23.28% of steers weigh between 1000 and 1100 pounds.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $\begin{array}{l}{z}_1=\frac{1000-1152}{84}=-1.8095\\ z_2=\frac{1100-1152}{84}=-0.619\end{array}$

  $\begin{array}{l}P(-1.8095<Z<-0.619)=P(Z<-0.619)-P(Z<-1.8095)\\ P(-1.8095<Z<-0.619)=0.2679-0.0352=0.2328\end{array}$

Hence, the 23.28% of steers weigh between 1000 and 1100 pounds.