Answer: B
Step-by-step explanation:
Answer:
[0.875;0.925]
Step-by-step explanation:
Hello!
You have a random sample of n= 400 from a binomial population with x= 358 success.
Your variable is distributed X~Bi(n;ρ)
Since the sample is large enough you can apply the Central Limit Teorem and approximate the distribution of the sample proportion to normal
^ρ≈N(ρ;(ρ(1-ρ))/n)
And the standarization is
Z= ^ρ-ρ ≈N(0;1)
√(ρ(1-ρ)/n)
The formula to estimate the population proportion with a Confidence Interval is
[^ρ ±
*√(^ρ(1-^ρ)/n)]
The sample proportion is calculated with the following formula:
^ρ= x/n = 358/400 = 0.895 ≅ 0.90
And the Z-value is
≅ 1.65
[0.90 ± 1.65 * √((0.90*0.10)/400)]
[0.875;0.925]
I hope you have a SUPER day!
Answer:
No, it is a reflection and a translation
Step-by-step explanation:
It reflects off of A and translates to the right over B
Answer:
p(b = 1) = 0.4096 = 40.96%
Step-by-step explanation:
For each candy, there are only two possible outcomes. Either it is blue, or it is not. The probability of a candy being blue is independent of any other candy. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![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)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![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)
And p is the probability of X happening.
20% are blue
This means that ![p = 0.2](https://tex.z-dn.net/?f=p%20%3D%200.2)
Sample of 4
This means that
.
Which of the following would find p(b=1)?
P(X = 1). So
![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 = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B4%2C1%7D.%280.2%29%5E%7B1%7D.%280.8%29%5E%7B3%7D%20%3D%200.4096)
So, p(b = 1) = 0.4096 = 40.96%
![2x+3x+4x=180](https://tex.z-dn.net/?f=2x%2B3x%2B4x%3D180)
would be the equation
You could refine it to make
![9x=180](https://tex.z-dn.net/?f=9x%3D180)
Divide both sides by 9
![9x/9=180/9](https://tex.z-dn.net/?f=9x%2F9%3D180%2F9)
This gives you
![x=20](https://tex.z-dn.net/?f=%20x%3D20)
Hope this helps!
;)