Plastic parts produced by an injection-molding operation are checked for conformance to specifications. each tool contains 15 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. an inspector chooses 3 part(s) from among the 15 at random. three cavities are affected by a temperature malfunction that results in parts that do not conform to specifications. round your answers to four decimal places. a. what is the probability that the inspector finds exactly one nonconforming part? b. what is the probability that the inspector finds at least one nonconforming part? c. what is the probability that the inspector finds at least two nonconforming part?

a) 0.4352

b) 0.5165

c) 0.0813

Step-by-step explanation:

In this problem we have 3 defective parts scattered among 15 parts.

We are going to select 3 out of 15 without replacement, so the situation can be modeled with the Hypergeometric distribution.

If X is the random variable that measures the number of defective parts in a sample of 3, the probability of selecting exactly k defective parts out of 15 would be given by

a) what is the probability that the inspector finds exactly one nonconforming part?

Replacing k with 1 in our previous formula, we get

b) what is the probability that the inspector finds at least one nonconforming part?

This would be P(X=1)+P(X=2)+P(X=3) = 1 - P(X=0).  

so 1 - P(X=0) = 1 - 0.4835 = 0.5165

c) what is the probability that the inspector finds at least two nonconforming part?

P(X=2) + P(X=3) = 1 - (P(X=0) + P(X=1)) = 1 - (0.4835 + 0.4352) =

= 1 - 0.9187 = 0.0813

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.