Final answer:
a) Probability (P(X < 1.01)\approx 0.7235,
b) P(X > 1.01)\approx 0.2765,
c) P(0.57 < X < 1.01)\approx 0.4937,
d) Expected time (E(X)\approx 1.1548,
e) E(X^2)\approx 1.4616,
f) Variance (Var(X)\approx 0.0445.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the area of probability and statistics.
The grade level is College, as the concepts of probability density functions, cumulative distribution functions, and normal distributions are typically encountered at this stage in education.
Within the detailed answer, we can discuss various concepts such as calculating probabilities from a probability density function, understanding uniform distributions, computing the mean and standard deviation for a dataset, and working with exponential distributions.
Additionally, we can tackle percentiles and median in the context of normal distributions, and deal with discrete probability distribution functions. These topics are central to college-level probability and statistics courses.
Your correct question is: Trainees must complete a specific task in less than 2 minutes. Consider the probablity density function below for the time it takes a trainee complete the task. f(x)=0.79−0.29x 0<x<2 a) What is the probability a traince will complete the task in less than 1.01 minutes? Give your answer to four decimal places. b) What is the probability that a trainee will complete the task in more than 1.01 minutes? Give your answer to four decimal places. c) What is the probability it will take a trainee between 0.57 minutes and 1.01 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 Vor( X ? Give your answer to four decimal places.