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# Rectangular plates are manufactured whose lengths are ISBN: 9780073401331 38

## Solution for problem 3E Chapter 4.12

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

Rectangular plates are manufactured whose lengths are distributed N(2.0, 0.12) and whose widths are distributed N(3.0 0.22). 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

c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally distributed?

Step-by-Step 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.

Step 2 of 4:

We have to estimate the mean and variance of A by using a simulated of sample size 1000.

Let X denote the length of the rectangular plate, and Y denote the width of the rectangular plate.

It is given that X~N(2.0,0.1 ), and Y~N(3.0, ). We can simulate a sample of 1000 by using minitab software as:

Calc- Random data- distribution- parameters(with sample size) - ok (store the data in column 1 and column 2 respectively). Since it is given that X and Y are independent

E(XY) =E(X) E(Y)

= 2 3

=  6

The simulation results will be approximate. That will change according to the sample.We can find the mean and variance of XY by using minitab as:

Find the column XY

Stat- Basic statistics - Display descriptive statistics- select the variable(XY)- statistics-ok.  (exactly), , Therefore the estimate of mean and variance of the area of rectangle A are and .

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The full step-by-step solution to problem: 3E from chapter: 4.12 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “Rectangular plates are manufactured whose lengths are distributed N(2.0, 0.12) and whose widths are distributed N(3.0 0.22). 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________________c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally distributed?” is broken down into a number of easy to follow steps, and 71 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 3E from 4.12 chapter was answered, more than 426 students have viewed the full step-by-step answer. This full solution covers the following key subjects: distributed, plate, whose, Probability, area. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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