Solution Found!
Rectangular plates are manufactured whose lengths are
Chapter 4, Problem 3E(choose chapter or problem)
Rectangular plates are manufactured whose lengths are distributed \(N(2.0, 0.1^2)\) and whose widths are distributed \(N(3.0,0.2^2)\). Assume the lengths and widths are independent. The area of a plate is given by \(A = XY\).
a. Use a simulated sample of size 1000 to estimate the mean and variance of A.
b. Estimate the probability that \(P(5.9<A<6.1)\).
c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally
distributed?
Equation Transcription:
Text Transcription:
N(2.0, 0.1^2)
N(3.0,0.2^2)
A=XY
P(5.9<A<6.1)
Questions & Answers
QUESTION:
Rectangular plates are manufactured whose lengths are distributed \(N(2.0, 0.1^2)\) and whose widths are distributed \(N(3.0,0.2^2)\). Assume the lengths and widths are independent. The area of a plate is given by \(A = XY\).
a. Use a simulated sample of size 1000 to estimate the mean and variance of A.
b. Estimate the probability that \(P(5.9<A<6.1)\).
c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally
distributed?
Equation Transcription:
Text Transcription:
N(2.0, 0.1^2)
N(3.0,0.2^2)
A=XY
P(5.9<A<6.1)
ANSWER:
Solution:
Step 1 of 4:
The length of manufactured rectangular plates are distributed N(2.0,0.12), and whose width are distributed N(3.0,0.22). The lengths and widths are independent. The area of the plate is given by
A= XY.