Trainees must complete a specific task in less than 2 minutes. consider the probability density function below for the time it takes a trainee to complete the task. f(x) = 0.85 - 0.35x0 < x < 2a) what is the probability a trainee will complete the task in less than 1.31 minutes? give your answer to four decimal places. b) what is the probability that a trainee will complete the task in more than 1.31 minutes? give your answer to four decimal places. c) what is the probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task? give your answer to four decimal places. d) what is the expected time it will take a trainee to complete the task? give your answer to four decimal places. e) if x represents the time it takes to complete the task, what is e(x2)? give your answer to four decimal places. f) if x represents the time it takes to complete the task, what is var(x)? give your answer to four decimal places.

a) 0.8132 or 81.32%

b) 0.1868 or 18.68%

c) 0.6116 or 61.16%

d) 0.7667 minutes

e) 0.8667 minutes

f) 0.1 minutes

Step-by-step explanation:

a)

If f(x) = 0.85-0.35x (0<x<2) is the PDF and X is the random variable that measures the time it takes for a trainee to complete the task, the probability a trainee will complete the task in less than 1.31 minutes is P(X<1.31)

b)

The probability that a trainee will complete the task in more than 1.31 minutes is  

P(X>1.31) = 1 - P(X<1.31) = 1 - 0.8132 = 0.1868

c)

The probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task is P(0.25<X<1.31)  

d)

the expected time it will take a trainee to complete the task

is E(X)

e)

f)

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

i think 5 miles per hour

step-by-step explanation: