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)/1.13 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.

Answer 1

E(X) = 3.565

c = 3.8475

0.4955

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