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) / 1.13 3 < x < 4.13

1 x > 4.13

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

What is the value c such that P (X < c) = 0.75? Give your answer to four decimal places.

What is the probability that X falls within 0.28 minutes of its mean? Give your answer to four decimal places.

E (X) = 3.565

c = 3.8475

0.4955

Step-by-step explanation:

The given cumulative distribution function is

F (x) = 0 for x < 3

F (x) = (x-3) / 1.13 for 3 < x < 4.13

F (x) = 1 for x > 4.13

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

E (X) = (a + b) / 2

E (X) = (3 + 4.13) / 2

E (X) = 3.565

What is the value c such that P (X < c) = 0.75? Give your answer to four decimal places.

P (X < c) = (c-3) / 1.13 = 0.75

c-3 = 0.75*1.13

c = 3 + 0.75*1.13

c = 3.8475

What is the probability that X falls within 0.28 minutes of its mean? Give your answer to four decimal places.

P (3.565 - 0.28 < X < 3.565 + 0.28)

F (3.565 + 0.28) - F (3.565 - 0.28)

(3.845-3) / 1.13 - (3.285-3) / 1.13

0.7477 - 0.2522

0.4955

Hence there is 49.55% probability that X will fall within 0.28 minutes of its mean