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

Question

Solve the problem.
-If a continuous uniform distribution has parameters of $\mu = 0 \text { and } \sigma = 1$ then the minimum is $- \sqrt { 3 }$ and the maximum is $\sqrt { 3 }$ . For this distribution, find $\mathrm { P } ( - 1 < \mathrm { x } < 0.5 )$ Round your answer to three decimal places.
A) 0.289
B) 0.577
C) 0.433
D) 0.25

Quizplus · Accepted Answer

The continuous uniform distribution is a rectangular-shaped distribution that is uniform across its range. Since $\mu = 0 $ and $\sigma =1$ for this distribution, we know that the range is from $-\sqrt{3}$ to $\sqrt{3}$.

To find $\mathrm{ P } ( - 1 < \mathrm{ x } < 0.5 )$, we need to find the area under the curve between $-1$ and $0.5$. We can do this by finding the proportions of the range that are represented by these values and subtracting the areas of the two triangles that are formed outside of this range:

$\mathrm{ P } ( - 1 < \mathrm{ x } < 0.5 ) = \frac{0.5 - (-1)}{\sqrt{3} - (-\sqrt{3})} - 2(\frac{0.5 - (-\sqrt{3})}{2(\sqrt{3})}) = \frac{1.5}{2\sqrt{3}} - 2(\frac{\sqrt{3} + 0.5}{2\sqrt{3}}) \approx 0.433$

Therefore, the best choice is C.

Solve the Problem μ=0 and σ=1\mu = 0 \text { and } \sigma = 1μ=0 and σ=1

Solve the Problem $\mu = 0 \text { and } \sigma = 1$