An article gives arguments for why fracture toughness in concrete specimens should have a Weibull distribution and presents several histograms of data that appear well fit by superimposed Weibull curves. Consider the following sample of size n = 18 observations on toughness for high-strength concrete (consistent with one of the histograms); values of pi = (i − 0.5) 18 are also given. Observation 0.47 0.60 0.65 0.6 0.72 0.74
Pi 0.0278 0.0833 0.1389 0.1944 0.25 0.3056
Observation 0.76 0.79 0.80 0.8 0.82 0.84
Pi 0.3611 0.4167 0.4722 0.5278 0.5833 0.6389
Observation 0.86 0.89 0.91 0.95 .01 1.05
Pi 0.6944 0.75 0.8056 0.8611 0.9167 0.9722
Construct a Weibull probability plot.

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step-by-step explanation:

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be