Area= base x height
So, the base is 9 1/4 and the height is 18 feet
so, the Area= 9 1/4 x 18
9 1/4 x 18
= 166.5
Using the binomial distribution, the probabilities are given as follows:
a. 0.2637 = 26.37%.
b. 0.8965 = 89.65%.
c. 0.0148 = 1.48%.
<h3>What is the binomial distribution formula?</h3>
The formula is:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
The values of the parameters for this problem are:
n = 5, p = 0.25.
Item a:
The probability is P(X = 2), hence:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B5%2C2%7D.%280.25%29%5E%7B2%7D.%280.75%29%5E%7B3%7D%20%3D%200.2637)
Item b:
The probability is:
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29)
In which:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B5%2C0%7D.%280.25%29%5E%7B0%7D.%280.75%29%5E%7B5%7D%20%3D%200.2373)
![P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B5%2C1%7D.%280.25%29%5E%7B1%7D.%280.75%29%5E%7B4%7D%20%3D%200.3955)
![P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B5%2C2%7D.%280.25%29%5E%7B2%7D.%280.75%29%5E%7B3%7D%20%3D%200.2637)
Then:
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%3D%200.2373%20%2B%200.3955%20%2B%200.2637%20%3D%200.8965)
Item c:
The probability is:
![P(X \geq 4) = P(X = 4) + P(X = 5)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%204%29%20%3D%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29)
In which:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0147](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B5%2C4%7D.%280.25%29%5E%7B4%7D.%280.75%29%5E%7B1%7D%20%3D%200.0147)
![P(X = 5) = C_{5,1}.(0.25)^{5}.(0.75)^{0} = 0.0001](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B5%2C1%7D.%280.25%29%5E%7B5%7D.%280.75%29%5E%7B0%7D%20%3D%200.0001)
Then:
![P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0147 + 0.0001 = 0.0148](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%204%29%20%3D%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29%20%3D%200.0147%20%2B%200.0001%20%3D%200.0148)
More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:
V= 628.32
Step-by-step explanation:
Answer:
22.9 yd
Step-by-step explanation:
You add them up and then you divide and you get your answer