Question

the values of a particular distribution are uniformly distributed between 4 and 8.

p(6 < x < 7) = \boxed{}

Explanation:

Step1: Recall Uniform Distribution Formula

For a uniform distribution between \(a\) and \(b\), the probability density function is \(f(x)=\frac{1}{b - a}\) for \(a\leq x\leq b\), and the probability \(P(c < x < d)\) (where \(a\leq c < d\leq b\)) is \((d - c)\times f(x)\), which simplifies to \(\frac{d - c}{b - a}\).

Step2: Identify Values

Here, \(a = 4\), \(b = 8\), \(c = 6\), \(d = 7\).

Step3: Calculate Probability

Substitute into the formula: \(\frac{7 - 6}{8 - 4}=\frac{1}{4}=0.25\).

Answer:

\(0.25\)