1. For the paint can question on page 207, in your textbook 4.22 you were provid

Question

1. For the paint can question on page 207, in your textbook 4.22 you were provided with the f distribution with a mean of 25 square feet and a standard deviation of 3 square feet. Suppose also that you buy a that can be painted using asingle Can of spray is slightly variable and follows a nearly normal three cans of spray paint. Let the random variable X be the amount of area covered by one entire can of paint. (a) How much area would you expect to cover with these three cans of spray paint? Use appropriate sym bolism to answer the question. . 25 si o. 3 (+. your simulation what did you get as the estimate expected amount of area covered by the three cans of paint? Again use appropriate symbolism to write your result. (c) What is the theoretical standard deviation for the distribution that has all the possible totals for the area covered by the three cans of paint? What did your simulation provide you with? (d) In your simulation what did you find was the distribution of the total area covered by three cans of paint? How do you know?

Explanation / Answer

here lets denote cans by X1 X2 X3 each following normal( mean 25 SD 3)

part a)

we expect that three cans will cover area equal to E(X1+X2+X3)=75. (THEORITICAL MEAN)

part B)

by simulation we get total of three can as E(X1+X2+X3)=77.35

part C)

theoritical SD of (X1+X2+X3) = root (VAR(X1+X2+X3))= ROOT(9+9+9)=5.19

by simulation we get SD of total as SD(X1+X2+X3)=2.66

part D)

in my simulation (running 10000times ) the distribution of the total area covered by three cans is approximately normal

its summary is

Min. 1st Qu. Median Mean 3rd Qu. Max.
20.14 25.97 71.61 58.36 76.82 91.24

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