Respuesta :
Answer:
The required probability is 0.1667
Step-by-step explanation:
Consider the provided information.
According to Probability Density Function: [tex]f(x)\left\{\begin{matrix} \frac{1}{b-a}& a<x<b\\ 0 & elsewhere\end{matrix}\right.[/tex]
Therefore,
[tex]f(x)\left\{\begin{matrix} \frac{1}{0.030}& -0.015<x<0.015\\ 0 & elsewhere\end{matrix}\right.[/tex]
The probability that such errors will be between –0.002 and 0.003 is:
[tex]P(-0.002\leq x\leq 0.003)=\int\limits^{0.003}_{-0.002} {\frac{1}{0.030}} \, dx[/tex]
[tex]P(-0.002\leq x\leq 0.003)=\frac{1}{0.030}[x]^{0.003}_{-0.002}[/tex]
[tex]P(-0.002\leq x\leq 0.003)=\frac{0.003+0.002}{0.030}=0.1667[/tex]
Hence, the required probability is 0.1667
