Use the data to solve the problem below: 243, 236, 389, 628, 143, 417, 205, 404,

Question

Use the data to solve the problem below:

243, 236, 389, 628, 143, 417, 205, 404, 464, 605, 137, 123, 372, 439, 497, 500, 535, 577, 441, 231, 675, 132, 196, 217, 660, 569, 865, 725, 457, 347 a) Computes the mean and standard deviation of the data. c) Uses the computed mean and standard deviation to estimate the upper and lower limits of strength for approximately 68 % of the samples (approximately 68% 0.5 % of the structural timber has a tested strength within the given limits). Assume that these measurements are Normally Distributed (use the Normal/Gaussian density function). d) Uses the computed mean and standard deviation to estimate the upper and lower limits of strength for approximately 96 % of the samples. Assume that these measurements are Normally Distributed (use the Normal/Gaussian density function) Computes the percentage of the sampled data that is actually between the estimated limits. e)

Explanation / Answer

Mean = (243 + 236 + 389 + 628 143 + 417 + 205 + 404 + 464 + 605 + 137 + 123 + 372 + 439 + 497 + 500 + 535 + 577 + 441 + 231 + 675 + 132 + 196 + 217 + 660 + 569 + 865 + 725 + 457 + 347)/30 = 414.3

Variance = ( (243 - 414.3)^2 + (236 - 414.3)^2 + (389 - 414 .3)^2 + (628 - 414.3)^2 +(143 - 414.3)^2 + (417 - 414.3)^2 + (205 - 414.3)^2 + (404 - 414.3)^2 + (464 - 414.3)^2 + (605 - 414.3)^2 + (137 - 414.3)^2+ (123 - 414.3)^2+ (372 - 414.3)^2+ (439 - 414.3)^2 + (497 - 414.3)^2+ (500 - 414.3)^2+ (535 - 414.3)^2 + (577 - 414.3)^2+ (441 - 414.3)^2 + (231 - 414.3)^2 + (675 - 414.3)^2 + (132 - 414.3)^2 + (196 - 414.3)^2 + (217 - 414.3)^2 + (660- 414.3)^2 + (569 - 414.3)^2+ (865 - 414.3)^2 + (725 - 414.3)^2 + (457 - 424.3)^2 + (347 - 414.3)^2)/30 = 38068.22

Standard deviation = 195.11

C) At 68% Confidence interval the critical value is 0.41

The confidence interval is

Mean +/- z* * SD/sqrt(n)

= 414.3 +/- 0.41 * 195.11/sqrt(30)

= 414.3 +/- 14.61

= 399.69, 428.91

D) At 96% Confidence interval the critical value is 2.05

The Confidence interval is

Mean +/- z* * SD/sqrt(n)

= 414.3 +/- 2.05 * 195.11/sqrt(30)

= 414.3 +/- 73.025

= 341.275, 487.325

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