Given: \(f(x) = \frac{1}{8} e^{-x/8}\ for\ x \geq 0 \mu = 8\)

Formula exponential probability:

\(P(x \leq a) = 1 - e^{-a/ \mu}\)

\(P(a < x < b) = e^{-a/ \mu} - e^{-b/ \mu}\)

Detetmine the probabilities:

\(a. P(x \leq 6) = 1 - e^{-6/8} \approx 0.5276\)

\(b. P(x \leq 4) = 1 - e^{-4/8} \approx 0.3935\)

\(с. P(x \geq 6) = e^{-6/8} \approx 0.4724\)

\(d. P(4 \leq x \leq 6) = e^{-4/8} - e^{-6/8} \approx 0.1342\)

Formula exponential probability:

\(P(x \leq a) = 1 - e^{-a/ \mu}\)

\(P(a < x < b) = e^{-a/ \mu} - e^{-b/ \mu}\)

Detetmine the probabilities:

\(a. P(x \leq 6) = 1 - e^{-6/8} \approx 0.5276\)

\(b. P(x \leq 4) = 1 - e^{-4/8} \approx 0.3935\)

\(с. P(x \geq 6) = e^{-6/8} \approx 0.4724\)

\(d. P(4 \leq x \leq 6) = e^{-4/8} - e^{-6/8} \approx 0.1342\)