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Bogdan [553]
1 year ago
5

Many urban zoos are looking at ways to effectively handle animal waste. One zoo has installed a facility that will transform ani

mal waste into electricity. To estimate how many pounds of waste they may have to fuel the new facility they began keeping meticulous records. They discovered that the amount of animal waste they were disposing of daily is approximately Normal with a mean of 348.5 pounds and a standard deviation of 38.2 pounds. Amounts over 350 pounds would generate enough electricity to cover what is needed to for the entire aquarium that day. Approximately what proportion of the days can the zoo expect to obtain enough waste to cover what is needed to run the entire aquarium for the day?
(A) 0.484
(B) 0.499
(C) 0.516
(D) 0.680
(E) 0.950
Mathematics
1 answer:
Zolol [24]1 year ago
8 0

Answer: The correct answer is (A).

Step-by-step explanation:

Let X = the amount of waste produced in a given day. X follows a distribution that is approximately Normal with a mean of 348.5 pounds and a standard deviation of 38.2 pounds.

P(X > 350) = Normalcdf(lower: 350, upper: 1000, mean: 348.5, SD: 38.2) = 0.484.

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The correct answer would be choice A: 1.

When 3 coins are flipped, there are 8 possible outcomes.

0 Tails = 1 ways
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2 Tails = 3 ways
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4 0
2 years ago
Answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sergeu [11.5K]

Answer:

Step-by-step explanation:

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6 0
2 years ago
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The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution
oksian1 [2.3K]

Answer:

a. P(X ≤ 5) = 0.999

b. P(X > λ+λ) = P(X > 2) = 0.080

Step-by-step explanation:

We model this randome variable with a Poisson distribution, with parameter λ=1.

We have to calculate, using this distribution, P(X ≤ 5).

The probability of k pipeline failures can be calculated with the following equation:

P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k!

Then, we can calculate P(X ≤ 5) as:

P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999

The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:

P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080

4 0
2 years ago
With food prices becoming a great issue in the world; wheat yields are even more important. Some of the highest yielding dry lan
Rzqust [24]

Answer:

Option E) 61.6

Step-by-step explanation:

We are given the following information in the question:

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Standard Deviation, σ = 30 bushels per acre

We assume that the distribution of yield is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(X>x) = 0.90

We have to find the value of x such that the probability is 0.90

P(X > x)  

P( X > x) = P( z > \displaystyle\frac{x - 100}{30})=0.90  

= 1 -P( z \leq \displaystyle\frac{x - 100}{30})=0.90  

=P( z \leq \displaystyle\frac{x - 100}{30})=0.10  

Calculation the value from standard normal table, we have,  

P(z

\displaystyle\frac{x - 100}{30} = -1.282\\x = 61.55 \approx 61.6  

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7 0
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"On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wi
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0.25 inches represents 1 mile

----------------------------------------------
Find 1 inch:
----------------------------------------------
1 inch represents 1 ÷ 0.25 miles
1 inch represents 4 miles

----------------------------------------------
Find 3.75 inches:
----------------------------------------------
1 inch represents 4 miles
3.75 inches represent 4 x 3.75 miles
3.75 inches represent 15 miles

----------------------------------------------
Find 2.25 inches:
----------------------------------------------
1 inch represents 4 miles
2.25 inches represent 4 x 2.25 miles
2.25 inches represent 9 miles

----------------------------------------------
Find Area:
----------------------------------------------
Area = Length x Width
Area = 15 x 9 
Area = 135 miles²

----------------------------------------------
Answer: 135 miles²
----------------------------------------------
6 0
2 years ago
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