Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability of observing exactly 3 tails.
<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.
In this problem, considering 3 tosses of a fair coin, the parameters are n = 3 and p = 0.5.
The probability of 3 tails is P(X = 3), 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 = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B3%2C3%7D.%280.5%29%5E%7B3%7D.%280.5%29%5E%7B0%7D%20%3D%200.125)
0.125 = 12.5% probability of observing exactly 3 tails.
More can be learned about the binomial distribution at brainly.com/question/24863377
Answer:
3.48 rounded to the nearest hundredth would be 3 I think
<em>Hope I Helped</em>
Answer:
in the form
would be:
![g(x)=(x-0)^2+7](https://tex.z-dn.net/?f=g%28x%29%3D%28x-0%29%5E2%2B7)
Step-by-step explanation:
Given:
Parent function:
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
Translation occurs 7 units up to get ![g(x)](https://tex.z-dn.net/?f=g%28x%29)
Translation Rules:
If
the function shifts
units to the up.
If
the function shifts
units to the down.
So, from the above rules
can be represented as:
[7 units up]
![g(x)=x^2+7](https://tex.z-dn.net/?f=g%28x%29%3Dx%5E2%2B7)
Writing
in the form
where
are integers.
![g(x)=1(x-0)^2+7](https://tex.z-dn.net/?f=g%28x%29%3D1%28x-0%29%5E2%2B7)
![g(x)=(x-0)^2+7](https://tex.z-dn.net/?f=g%28x%29%3D%28x-0%29%5E2%2B7)
Answer:
15
Step-by-step explanation:
38/2.5=15.2
Round it to 15