Let X represent the time it takes from when someone enters the line for a roller
ID: 3208228 • 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. 0 x 4.47 a) What is E(X)? Give your answer to three decimal places. | | b) What is the value c such that P(X lessthanorequalto c) = 0.67? Give your answer to four decimal places. c) What is the probability that X falls within 0.4 minutes of its mean? Give your answer to four decimal places.Explanation / Answer
Solution:
a) f(x) = 1/1.47 3<x<4.47
E(X) = integral of x.f(x) = x/1.47 from 3 to 4.47 in this case which works out to be
4.47^2/(2*1.47) -3^2/(2*1.47) = 3.735
Alternatively, you could recognize that the distribution above Uniform on 3 to 4.47,
so the mean is (3+4.47)/2 = 3.735.
b) F(c)=P(X<c) = (c-3)/1.47 = 0.67 for c. So, c= 3+1.47*0.67 = 3.9849
c) P(3.735-0.4 < X < 3.735 + 0.4) = F(3.735 + 0.4) - F(3.735 - 0.4) = 2* 0.4/1.47
= 0.5442
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