Chapter 3.2, Problem 3.37E

(a)

To determine

To find the proportion of bags weighed less than 10.25 pounds.

Answer to Problem 3.37E

P( x < 10.25) = 0.69146

Explanation of Solution

Given:

  $\text{Bags weight ~ N(10, 0}\text{.5)}$

Calculation:

  $\begin{array}{l}P\left(x<10.25\right)\\ =P\left(\frac{x-\mu }{\sigma }<\frac{10.25-10}{0.5}\right)\\ =P\left(z<0.5\right)\\ =0.69146\end{array}$

(b)

To determine

To find the proportion of bags weighed between 9.5 and 10.25 pounds.

Answer to Problem 3.37E

P (9.5 <x< 10.25) = 0.5328

Explanation of Solution

Given:

  $\text{Bags weight ~ N(10, 0}\text{.5)}$

Calculation:

  $\begin{array}{l}P\left(9.5<x<10.25\right)\\ =P\left(\frac{9.5-10}{0.5}<\frac{x-\mu }{\sigma }<\frac{10.25-10}{0.5}\right)\\ =P\left(-1<z<0.5\right)\\ =P(z<0.5)-P(z<-1)\\ =0.69146-[1-0.84134]\\ =0.5328\end{array}$