Answer:
a) E(x)=3.565
b) c=3.8475 --> P(X < 3.8475) = 0.75
c) The probability that X falls above or below 0.28 min from the mean is P=0.4954.
Step-by-step explanation:
We have the cumulative distribution function as information.
a) To calculate the expected value, we can calculate the value of x in which F(x) equals 0.5. This happens for x=3.565.
b) What is the value c such that P(X < c) = 0.75?
In this case, we have to calculate x to have F(x)=0.75
This happens for x=3.8475.
c) We have to calculate the probability that X falls above or below 0.28 min from the mean (x=3.565).
This is the probability that the time is between 3.285 and 3.845
We can calculate this as:
The probability that X falls above or below 0.28 min from the mean is P=0.4954.