Using the binomial distribution, the probabilities are given as follows:
a) 0.4159 = 41.59%.
b) 0.5610 = 56.10%.
c) 0.8549 = 85.49%.
<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.
For this problem, the values of the parameters are:
n = 3, p = 0.76.
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_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B3%2C2%7D.%280.76%29%5E%7B2%7D.%280.24%29%5E%7B1%7D%20%3D%200.4159)
Item b:
The probability is P(X < 3), hence:
P(X < 3) = 1 - P(X = 3)
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 = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B3%2C3%7D.%280.76%29%5E%7B3%7D.%280.24%29%5E%7B0%7D%20%3D%200.4390)
Then:
P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.
Item c:
The probability is:
![P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%3D%200.4159%20%2B%200.4390%20%3D%200.8549)
More can be learned about the binomial distribution at brainly.com/question/24863377
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9514 1404 393
Answer:
C. 0.98
Step-by-step explanation:
The attached graph shows the constraints. The feasible solution space is the doubly-shaded area in the first quadrant. The negative coefficients on x and y suggest that the objective function will be maximized when x and y are minimized. The solution space vertex that does that is ...
(x, y, Y) = (6, 4, 0.98)
Answer:
g = (2-x)/3
Step-by-step explanation:
PLS GIVE BRAINLIEST
Answer:
Well B is the base of the shape
If thats what you mean
Step-by-step explanation:
Answer:
Solving the equation for all real solutions in simplest form.
we get ![\mathbf{z=10.9\: or\: z=1.1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bz%3D10.9%5C%3A%20or%5C%3A%20z%3D1.1%7D)
Step-by-step explanation:
We need to solve the equation for all real solutions in simplest form.
![z^2 - 12z +9= -3](https://tex.z-dn.net/?f=z%5E2%20-%2012z%20%2B9%3D%20-3)
First simplifying the equation:
![z^2 - 12z +9+3= -3+3\\z^2 - 12z +12= 0](https://tex.z-dn.net/?f=z%5E2%20-%2012z%20%2B9%2B3%3D%20-3%2B3%5C%5Cz%5E2%20-%2012z%20%2B12%3D%200)
Now, we can solve the equation using quadratic formula:
![z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
we have a = 1, b=-12 and c=12
Putting values in formula and finding values of x
![z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\z=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\z=\frac{12\pm\sqrt{144-48}}{2}\\z=\frac{12\pm\sqrt{96}}{2}\\z=\frac{12\pm9.8}{2}\\z=\frac{12+9.8}{2}\:or\:z=\frac{12-9.8}{2}\\z=10.9\:or\:z=1.1](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5Cz%3D%5Cfrac%7B-%28-12%29%5Cpm%5Csqrt%7B%28-12%29%5E2-4%281%29%2812%29%7D%7D%7B2%281%29%7D%5C%5Cz%3D%5Cfrac%7B12%5Cpm%5Csqrt%7B144-48%7D%7D%7B2%7D%5C%5Cz%3D%5Cfrac%7B12%5Cpm%5Csqrt%7B96%7D%7D%7B2%7D%5C%5Cz%3D%5Cfrac%7B12%5Cpm9.8%7D%7B2%7D%5C%5Cz%3D%5Cfrac%7B12%2B9.8%7D%7B2%7D%5C%3Aor%5C%3Az%3D%5Cfrac%7B12-9.8%7D%7B2%7D%5C%5Cz%3D10.9%5C%3Aor%5C%3Az%3D1.1)
So, we get value of z: z=10.9 or z=1.1
Solving the equation for all real solutions in simplest form.
we get ![\mathbf{z=10.9\: or\: z=1.1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bz%3D10.9%5C%3A%20or%5C%3A%20z%3D1.1%7D)