Question

Let X represent the time it takes from when someone enters the line for a roller coaster until they exit on the other side. Consider the probability model defined by the cumulative distribution function given below.




0

x < 3



F(x)

=

(x-3)/1.22

3 < x < 4.22





1

x > 4.22




1.What is E(X)? Give your answer to three decimal places.

2.What is the value c such that P(X < c) = 0.76? Give your answer to four decimal places.


3.What is the probability that X falls within 0.14 minutes of its mean? Give your answer to four decimal places.