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Alisiya [41]
2 years ago
11

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
Mathematics
1 answer:
Ganezh [65]2 years ago
4 0

Answer:

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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