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Let X represent the time it takes from when someone enters the line for a roller

ID: 2900526 • Letter: L

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.


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

What is the value c such that P(X < c) = 0.33? Give your answer to four decimal places

What is the probability that X falls within 0.36 minutes of its mean? Give your answer to four decimal places.

0 x < 3 F(x) = (x-3)/1.45 3 < x < 4.45 1 x > 4.45

Explanation / Answer

E(x) = integral from x = 3 to x = 4.75: x f(x) dx, where f(x) = 1 / 1.75

E(x) = evaluate from x = 3 to x = 4.75: (x^2 / 2)(1/1.75) = 3.880

B) P(X <= c) = (c-3)/1.75 = 0.33, solve for c

c = 3.585185



C) . P(3.88-0.36<X<3.88+0.36) = integral f(x) =