Rope checks. In a certain manufacturing process, an automated quality control computer checks 10 yards of rope at a time. If no defects are detected in that 10-yard section, that portion of the rope is passed on. However, if there is a defect detected, a person will have to check the rope over more carefully to determine where (measured from the left side in yards) the defect is. If exactly
1 defect is detected in a rope section, we would like to find the probabilities for its location.
a. Why is this a Continuous Uniform problem?
b. What does X represent in this scenario?
c. What are the parameters in this scenario?
d. What is the expected value for the location of the defect?
e. What is the standard deviation?
f. What is the probability density function? Write it in function notation, and also graph it.
g. What is the cumulative distribution function? Write it in function notation, and also graph it.
h. Find P(X > 8).
i. Find P(2.3 ≤ X ≤ 5.2)
j. Find P(X