If a continuous uniform distribution has parameters of $\mu = 0$ and $\sigma = 1$, then the minimum is $- \sqrt { 3 }$ and the maximum is $\sqrt { 3 }$. For this distribution, find $\mathrm { P } ( - 1

Question

If a continuous uniform distribution has parameters of $\mu = 0$ and $\sigma = 1$, then the minimum is $- \sqrt { 3 }$ and the maximum is $\sqrt { 3 }$. For this distribution, find $\mathrm { P } ( - 1 < x < 1.5 )$. Round your answer to three decimal places.
A) 0.722
B) 0.417
C) 0.866
D) 0.577

Quizplus · Accepted Answer

The probability density function of a continuous uniform distribution is given by:$$f(x) = \frac{1}{b-a}, \quad a \le x \le b$$where $a$ and $b$ are the minimum and maximum values, respectively.In this case, $\mu = 0$ and $\sigma = 1$, so the minimum is $- \sqrt { 3 }$ and the maximum is $\sqrt { 3 }$. Therefore, the probability density function is:$$f(x) = \frac{1}{2\sqrt{3}}, \quad - \sqrt{3} \le x \le \sqrt{3}$$The probability of $x$ being between -1 and 1.5 is:$$P(-1 < x < 1.5) = \int_{-1}^{1.5} \frac{1}{2\sqrt{3}} dx = \frac{1}{2\sqrt{3}} \left[ x \right]_{-1}^{1.5} = \frac{1}{2\sqrt{3}} (1.5 - (-1)) = \frac{1}{2\sqrt{3}} (2.5) = 0.722$$Therefore, the correct answer is A.

If a Continuous Uniform Distribution Has Parameters Of μ=0\mu = 0μ=0

If a Continuous Uniform Distribution Has Parameters Of $\mu = 0$