Rectangular plates are manufactured whose lengths are

Chapter 4, Problem 3E

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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)

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.


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