Answer:
Step-by-step explanation:
=0.4
because a objest cannot be wieghed negatively unless its lighter than air
If you would be nicer I would!
Using the binomial distribution, it is found that the probabilities are:
<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.
Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
Then:
![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_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B15%2C4%7D.%280.4%29%5E%7B4%7D.%280.6%29%5E%7B11%7D%20%3D%200.1228)
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
Then:
![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_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B12%2C2%7D.%280.2%29%5E%7B2%7D.%280.8%29%5E%7B10%7D%20%3D%200.2835)
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
![P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%203%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%2B%20P%28X%20%3D%203%29)
Using the binomial formula for each value and adding them:
![P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841](https://tex.z-dn.net/?f=P%28X%20%5Cleq%203%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%2B%20P%28X%20%3D%203%29%20%3D%200.3585%20%2B%200.3774%20%2B%200.1887%20%2B%200.0596%20%3D%200.9841)
More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:
x= 23.33
Step-by-step explanation:
7=x+2x-5-58
combine like terms
7=3x-63
add 63 to both sides
70=3x
divide by 3
x=23.33