Mathematics: In a certain experiment, the error made in determining the density of a substance is a random variable having a uniform density with a=-0.015 and b=0.015. find the probability that such errors will be between –0.002 and 0.003

In a certain experiment, the error made in determining

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10.01.2022

The required probability is 0.1667

Step-by-step explanation:

Consider the provided information.

According to Probability Density Function: $f(x)\left\{\begin{matrix} \frac{1}{b-a}& a$

Therefore,

$f(x)\left\{\begin{matrix} \frac{1}{0.030}& -0.015$

The probability that such errors will be between –0.002 and 0.003 is:

$P(-0.002\leq x\leq 0.003)=\int\limits^{0.003}_{-0.002} {\frac{1}{0.030}} \, dx$

$P(-0.002\leq x\leq 0.003)=\frac{1}{0.030}[x]^{0.003}_{-0.002}$

$P(-0.002\leq x\leq 0.003)=\frac{0.003+0.002}{0.030}=0.1667$

Hence, the required probability is 0.1667

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