2. the copper wire current measurement is said to be evenly distributed from 0 to 20 milliamperes (ma). a…

Explanation:

Step1: Identify distribution type

The current measurement is uniformly - distributed over the interval $[0,20]$. The probability density function of a uniform distribution $U(a,b)$ is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$ and $0$ otherwise. Here, $a = 0$ and $b = 20$, so $f(x)=\frac{1}{20}$ for $0\leq x\leq 20$ and $0$ otherwise.

Step2: Find the length of the distribution

The length of the distribution (range) is given by $b - a$. $b - a=20-0 = 20$

Step3: Calculate $P(X>15)$

For a uniform distribution $U(a,b)$, the probability $P(c<X<d)$ is given by $P(c<X<d)=\frac{d - c}{b - a}$ when $a\leq c<d\leq b$. $P(X>15)=\frac{20 - 15}{20}=\frac{5}{20}=0.25$

Step4: Calculate $P(2<X<10)$

Using the formula $P(c<X<d)=\frac{d - c}{b - a}$, with $c = 2$, $d = 10$, $a = 0$ and $b = 20$. $P(2<X<10)=\frac{10 - 2}{20}=\frac{8}{20}=0.4$

Answer:

a. The length of the distribution is 20. b. $P(X>15)=0.25$ c. $P(2<X<10)=0.4$