Chapter 6, Problem 4CURP

(a)

To determine

Find the value of $P\left(0\le x<30\right)$.

Answer to Problem 4CURP

The value of $P\left(0\le x<30\right)$ is 0.85.

Explanation of Solution

Calculation:

From table A, the Magnetic Susceptibility intervals and corresponding probabilities are,

Magnetic Susceptibility	$0\le x<10$	$10\le x<20$	$20\le x<30$	$30\le x<40$	$40\le x$
$P\left(x\right)$	0.25	0.45	0.15	0.10	0.05

The value of $P\left(0\le x<30\right)$ is,

$\begin{array}{c}P\left(0\le x<30\right)=P\left(0\le x<10\right)+P\left(10\le x<20\right)+P\left(20\le x<30\right)\\ =0.25+0.45+0.15\\ =0.85\end{array}$

Hence, the value of $P\left(0\le x<30\right)$ is 0.85.

(b)

To determine

Find the value of $P\left(10\le x<40\right)$.

Answer to Problem 4CURP

The value of $P\left(10\le x<40\right)$ is 0.70.

Explanation of Solution

Calculation:

The value of $P\left(10\le x<40\right)$ is,

$\begin{array}{c}P\left(10\le x<40\right)=P\left(10\le x<20\right)+P\left(20\le x<30\right)+P\left(30\le x<40\right)\\ =0.45+0.15+0.10\\ =0.70\end{array}$

Hence, the value of $P\left(10\le x<40\right)$ is 0.70.

(c)

To determine

Find the value of $P\left(x<20\right)$.

Answer to Problem 4CURP

The value of $P\left(x<20\right)$ is 0.70.

Explanation of Solution

Calculation:

The value of $P\left(x<20\right)$ is,

$\begin{array}{c}P\left(x<20\right)=P\left(0\le x<10\right)+P\left(10\le x<20\right)\\ =0.25+0.45\\ =0.70\end{array}$

Hence, the value of $P\left(x<20\right)$ is 0.70.

(d)

To determine

Find the value of $P\left(x\ge 20\right)$.

Answer to Problem 4CURP

The value of $P\left(x\ge 20\right)$ is 0.30.

Explanation of Solution

Calculation:

The value of $P\left(x\ge 20\right)$ is,

$\begin{array}{c}P\left(x\ge 20\right)=P\left(20\le x<30\right)+P\left(30\le x<40\right)+P\left(40\le x\right)\\ =0.15+0.10+0.05\\ =0.30\end{array}$

Hence, the value of $P\left(x\ge 20\right)$ is 0.30.

(e)

To determine

Find the value of $P\left(30\le x\right)$.

Answer to Problem 4CURP

The value of $P\left(30\le x\right)$ is 0.15.

Explanation of Solution

Calculation:

The value of $P\left(30\le x\right)$ is,

$\begin{array}{c}P\left(30\le x\right)=P\left(30\le x<40\right)+P\left(40\le x\right)\\ =0.10+0.05\\ =0.15\end{array}$

Hence, the value of $P\left(30\le x\right)$ is 0.15.

(f)

To determine

Find the value of $P\left(x\text{ not less than }10\right)$.

Answer to Problem 4CURP

The value of $P\left(x\text{ not less than }10\right)$ is 0.75.

Explanation of Solution

Calculation:

The value of $P\left(x\text{ not less than }10\right)$ is,

$\begin{array}{c}P\left(x\text{ not less than }10\right)=P\left(x\ge 10\right)\\ =P\left(10\le x<20\right)+P\left(20\le x<30\right)+P\left(30\le x<40\right)+P\left(40\le x\right)\\ =0.45+0.15+0.10+0.05\\ =0.75\end{array}$

Hence, the value of $P\left(x\text{ not less than }10\right)$ is 0.75.

(g)

To determine

Find the value of $P\left(0\le x<10\text{ or 40}\le x\right)$.

Answer to Problem 4CURP

The value of $P\left(0\le x<10\text{ or 40}\le x\right)$ is 0.30.

Explanation of Solution

Calculation:

The value of $P\left(0\le x<10\text{ or 40}\le x\right)$ is,

$\begin{array}{c}P\left(0\le x<10\text{ or 40}\le x\right)=P\left(0\le x<10\right)+P\left(40\le x\right)\\ =0.25+0.05\\ =0.30\end{array}$

Hence, the value of $P\left(0\le x<10\text{ or 40}\le x\right)$ is 0.75.

(h)

To determine

Find the value of $P\left(\text{40}\le xand\text{ 20}\le x\right)$.

Answer to Problem 4CURP

The value of $P\left(\text{40}\le xand\text{ 20}\le x\right)$ is 0.05.

Explanation of Solution

Calculation:

The value of $P\left(\text{40}\le xand\text{ 20}\le x\right)$ is,

$\begin{array}{c}P\left(\text{40}\le xand\text{ 20}\le x\right)=P\left(40\le x\right)\\ =0.05\end{array}$

Hence, the value of $P\left(\text{40}\le xand\text{ 20}\le x\right)$ is 0.05.