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# Probability-Multiple Choice for a Rock Crushing Company

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F.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another. How many tons of blasted rock should be stored at any of the plants per day such that the probability of running out of blasted rocks to crush is 0.05

1.) .2000 tons

2.) 11.98 tons

3.) 4.000 tons

4.) 1.040 tons

G.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another. What is the probability that two of the plants will crush more than 4 tons on a given day?

1.) 0.74

2.) 0.26

3.) 0.1369

4.) 0.1850

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F.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another. How many tons of blasted rock should be stored at any of the plants per day such that the probability of running out of blasted rocks to crush is 0.05

1.) .2000 tons

2.) 11.98 tons

3.) 4.000 tons

4.) 1.040 tons

The formula for the cumulative distribution function of the exponential distribution is

F(x)= 1 - e -x / beta

Here beta = 4
We will calculate the cumulative probability for the different values of x

x= F(x)= probability of running out of blasted
0.2 0.0488 0.95 = 1- 0.0488
11.98 0.95 0.05 = 1- 0.95
4 0.6321 0.37 = 1- 0.6321
1.04 0.2289 0.77 = 1- 0.2289

G.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another. What is the probability that two of the plants will crush more than 4 tons on a given day?

1.) 0.74

2.) 0.26

3.) 0.1369

4.) 0.1850

F(x)= 1 - e -x / beta

Here beta = 4
We will calculate the cumulative probability for x=4

x= F(x)= probability of running out of blasted
4 0.6321 0.3679 = 1- 0.6321

probability that two of the plants will crush more than 4 tons on a given day?
This is a binommial distribution P(r)= ncr p r * q n-r
We will set n= 3 and r= 2
Probability that a plant will crush more than 4 tons=p= 0.3679
Probability that a plant will crush upto 4 tons=q= 0.6321 = 1- 0.3679

n= 3
p= 0.3679
q=1-p= 0.6321
r= 2
P(r)= ncr p r * q n-r =
r=
2 P(2)= 0.2567 =3*(0.3679^2)*(0.6321^1)

Therefore the answer is 2.) 0.26

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