Solution Found!
A process that manufactures piston rings produces rings
Chapter 2, Problem 16E(choose chapter or problem)
A process that manufactures piston rings produces rings whose diameters (in centimeters) vary according to the probability density function
\(f(x)= \begin{cases}3\left[1-16(x-10)^{2}\right] & 9.75<x<10.25 \\ 0 & \text { otherwise }\end{cases}\)
a. Find the mean diameter of rings manufactured by this process.
b. Find the standard deviation of the diameters of rings manufactured by this process. (Hint: Equation 2.36 may be easier to use than Equation 2.37.)
c. Find the cumulative distribution function of piston ring diameters.
d. What proportion of piston rings have diameters less than 9.75 cm?
e. What proportion of piston rings have diameters between 9.75 and 10.25 cm?
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise ^3[1-16(x-10)2] 9.75<x<10.25
Questions & Answers
QUESTION:
A process that manufactures piston rings produces rings whose diameters (in centimeters) vary according to the probability density function
\(f(x)= \begin{cases}3\left[1-16(x-10)^{2}\right] & 9.75<x<10.25 \\ 0 & \text { otherwise }\end{cases}\)
a. Find the mean diameter of rings manufactured by this process.
b. Find the standard deviation of the diameters of rings manufactured by this process. (Hint: Equation 2.36 may be easier to use than Equation 2.37.)
c. Find the cumulative distribution function of piston ring diameters.
d. What proportion of piston rings have diameters less than 9.75 cm?
e. What proportion of piston rings have diameters between 9.75 and 10.25 cm?
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise ^3[1-16(x-10)2] 9.75<x<10.25
ANSWER:
Answer:
Step 1 of 6:
Given the probability density function is
