The data for fracture toughness of steel plate are plotted on a normal probabili

Question

The data for fracture toughness of steel plate are plotted on a normal probability graph in the figure shown above. The ordinate is the standard normal variate. z. corresponding with each data point. The 25 observations were ranked from smallest (x_l = 69.5) to largest (x_25 = 93.7). The ordered observations X_j where then plotted against their observed z_j where z_j is found as the standard normal value corresponding to the observed cumulative frequency (j - 0.5 )/n. A line and its equation is shown: the line was determined with a method of moments style fit in the Z vs. X space. Based upon the plot, estimate the sample mean. Based upon the plot, estimate the sample standard deviation. Comment upon the appropriateness of both the line as a model for the fit and whether the normal distribution is an appropriate model.

Explanation / Answer

here z=0.303x-23.06 after solving and rearranging this equation we will have z=(x-75.9)/3.3

so by definition of standard normal variate

sample mean=75.9 and standard deviaion 3.3

answer of part(a)sample mean=75.9

answer of part(b) standard deviaion =3.3

answer of part(c)

model is fitted well as most of the points are on the line of regression and the mormal distribution is an appropriate model

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