2NB3 Components from three different manufacturers have been procured; 100 from Manufacturer A, of which 10% are defective; 300 from Manufacturer B, of which 5% are defective; and 500 from Manufacturer C, of which 20% are defective. We randomly select the shipment from one of the manufacturers and then randomly pick a component from it. (a) What is the probability that the selected component is defective

Step-by-step explanation:

Hello!

There are 3 Manufacturers of 2NB3 components:

Manufacturer A

X₁: Number of defective components manufactured by A in a sample of 100.

From 100 components, 10% are defective.

Manufacturer B

X₂: Number of defective components manufactured by B in a sample of 300.

From 300, 5% are defective.

Manufacturer C

X₃: Number of defective components manufactured by C in a sample of 500.

From 500, 20% are defective.

These three variables are discrete and meet the criteria of the binomial experiment.

Binomial criteria:

1. The number of observation of the trial is fixed. n₁=100, n₂= 300 and n₃= 500

2. Each observation in the trial is independent, this means that none of the trials will have an effect on the probability of the next trial. There are two possible observations "success" and "failure" In this experiment, for the three variables the "success" is finding a defective piece-

3. The probability of success in the same from one trial to another. p₁= 0.10, p₂=0.05 and p₃= 0.20

X₁~Bi(n₁;p₁)

X₂~Bi(n₂;p₂)

X₃~Bi(n₃;p₃)

Manufacturer A

P(X₁=1)

Manufacturer B

P(X₂=1)

Manufacturer C

P(X₃=1)

I hope it helps!

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

positive

step-by-step explanation:

the quadrant is facing upwards