Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0 (a) Write the formula for P(x ≤ x0). (b) Find P(x ≤ 4). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(4 ≤ x ≤ 6). (Round your answer to four decimal places.)

Question:

Consider the following exponential probability density function.

f(x) = 1/5e^(−x/5) for x ≥ 0

(a) Write the formula for P(x ≤ x0). (b) Find P(x ≤ 4). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(4 ≤ x ≤ 6). (Round your answer to four decimal places.)

(a) P(x ≤ x0) = 1 - e^(−x0/5)

(b) P(x ≤ 4) = 0.5506

(c) P(x ≥ 5) = 0.3678

(d) P(x ≤ 6) = 0.6988

(e) P(4 ≤ x ≤ 6) = 0.1482

Step-by-step explanation:

The standard form of the exponential probability density function is given by

f(x) = 1/μe^(−x/μ)

Where μ is the mean, for the given problem μ = 5

(a) Write the formula for P(x ≤ x0)

P(x ≤ x0) = 1 - e^(−x0/5)

(b) Find P(x ≤ 4)

P(x ≤ 4) = 1 - e^(−4/5)

P(x ≤ 4) = 1 - 0.4493

P(x ≤ 4) = 0.5506

(c) Find P(x ≥ 5)

P(x ≥ 5) = e^(−5/5)

P(x ≥ 5) = 0.3678

(d) Find P(x ≤ 6)

P(x ≤ 6) = 1 - e^(−6/5)

P(x ≤ 6) = 1 - 0.3011

P(x ≤ 6) = 0.6988

(e) Find P(4 ≤ x ≤ 6)

P(4 ≤ x ≤ 6) = e^(−4/5) - e^(−6/5)

P(4 ≤ x ≤ 6) = 0.4493 - 0.3011

P(4 ≤ x ≤ 6) = 0.1482

answer is 12345678900987654321234567890987654321

step-by-step explanation:

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )