A piece of rope is made up of 100 strands. Assume that the breaking strength of the rope is the sum of the breaking strengths of the individual strands. Assume further that this sum may be considered to be the sum of an independent trial process with 100 experiments each having an expected value of 10 pounds and standard deviation Find the approximate probability that the rope will support a weight
a. of 1000 pounds.
b. of 970 pounds.

a. of 1000 pounds. P=0.5

b. of 970 pounds. P=0.99865

Step-by-step explanation:

The question is incomplete: the standard deviation is 1.

The strength of the rope is the sum of the strengh of the 100 strands that make the rope. If the strands have a mean strength of 10 and a standard devition of 1, the strength of the rope will have the following mean and standard deviations:

We can calculate then, the probability that the rope will support a weight of 1000 pounds:

The probability that the rope will support a weight of 970 pounds is:

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