Respuesta :
Answer:
Step-by-step explanation:
Given that trainees must complete a specific task in less than 2 minutes.Consider the probability density function below for the time ittakes a trainee to complete the task.
[tex]f(x) = 0.67 - 0.17x, 0 < x < 2[/tex]
Hence F(x) = [tex]\int\limits^x_0 {f(x)} \, dx[/tex]= cumulative distributive function for x between 0 and 2.
1) the probability a trainee will complete the task inless than 1 minutes
=F(1) = 0.67-0.085 = 0.585
2. the probability that a trainee will complete the task inmore than 1 minutes
=1-F(1) = 0.415
3. the probability it will take a trainee between 0.68 minutes and 1 minutes to complete the task
=F(1)-F(0.68) =0.168704
=0.1687
4. the expected time it will take a trainee to complete thetask
=[tex]\int\limits^2_0 {x(0.67-0.17x)} \, dx \\=0.886667[/tex]
=0.8867
5.If X represents the time it takes to complete the task, what isE(X2)? Give your answer to four decimal places.
E(x^2) =
[tex]\int\limits^2_0 {x^2(0.67-0.17x)} \, dx \\=1.106667[/tex]
=1.1067
6.If X represents the time it takes to complete the task, what isVar(X)
Var(x) = E(x^2)-Mean^2
= 1.106667-0.886667^2
= 0.320489
=0.3205
