How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches

Question

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:

Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds. Give a 98% confidence interval for the mean load required to pull the wood apart.

33,190     31,860     32,590     26,520     33,280 32,320     33,020     32,030     30,460     32,700 23,040     30,930     32,720     33,650     32,340 24,050     30,170     31,300     28,730     31,920

Explanation / Answer

Solution:- Given following: 33190 31860 32590 26520 33280 32320 33020 32030 30460 32700 23040 30930 32720 33650 32340 24050 30170 31300 28730 31920

mean = sum of terms/no of terms

= 616820/20

= 30841

standard deviation = 3000

98% confidence interval for Z = 2.33

Standard Error (SE) = SD/sqrt(n) = 3000/sqnt 20 = 670.8204

98% confidence interval for the mean = 30841 +/- 2.33*(670.8204)

= (30841 - 1563.0115 ,  30841 + 1563.0115)

= (29277.9885 , 32404.0115 )

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