Please do part b 2.2.6A car panel is spray-painted by a machine, and the technicians areparticularly interested in the thickness of the resulting paint layer.Suppose that the random variable X measures the thickness of the paintin millimeters at a randomly chosen point on a randomly chosen carpanel, and that X takes values between 0.125 and 0.5 mm with aprobability density function off(x) = A(0.5 - (x -0.25)²)for 0.125 ≤ x ≤ 0.5 and f(x) = 0 elsewhere.(a) Find the value of A and sketch the probability density function.(b) Construct and sketch the cumulative distribution function.(c) What is the probability that the paint thickness at a particular point isless than 0.2 mm?

Answered: (b) Construct and sketch the cumulative…

Math

Probability

(b) Construct and sketch the cumulative distribution function.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 52CR

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Question

Please do part b

2.2.6A car panel is spray-painted by a machine, and the technicians are
particularly interested in the thickness of the resulting paint layer.
Suppose that the random variable X measures the thickness of the paint
in millimeters at a randomly chosen point on a randomly chosen car
panel, and that X takes values between 0.125 and 0.5 mm with a
probability density function of
f(x) = A(0.5 - (x -0.25)²)
for 0.125 ≤ x ≤ 0.5 and f(x) = 0 elsewhere.
(a) Find the value of A and sketch the probability density function.
(b) Construct and sketch the cumulative distribution function.
(c) What is the probability that the paint thickness at a particular point is
less than 0.2 mm?

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