Answer:
Step-by-step explanation:
i dont see an image
Answer:
x=48
Step-by-step explanation:
![84 + 2x = 180 \\ 2x = 96 \\ x = 48](https://tex.z-dn.net/?f=84%20%2B%202x%20%3D%20180%20%5C%5C%202x%20%3D%2096%20%5C%5C%20x%20%3D%2048)
Answer:
The probability of founding exactly one defective item in the sample is P=0.275.
The mean and variance of defective components in the sample are:
![\mu=0.375\\\\\sigma^2=0.347](https://tex.z-dn.net/?f=%5Cmu%3D0.375%5C%5C%5C%5C%5Csigma%5E2%3D0.347)
Step-by-step explanation:
In the case we have a lot with 3 defectives components, the proportion of defectives is:
![p=3/40=0.075](https://tex.z-dn.net/?f=p%3D3%2F40%3D0.075)
a) The number of defectives components in the 5-components sample will follow a binomial distribution B(5,0.075).
The probability of having one defective in the sample is:
![P(k=5)=\binom{5}{1}p^1(1-p)^4=5*0.075*0.925^4=0.275](https://tex.z-dn.net/?f=P%28k%3D5%29%3D%5Cbinom%7B5%7D%7B1%7Dp%5E1%281-p%29%5E4%3D5%2A0.075%2A0.925%5E4%3D0.275)
b) The mean and variance of defective components in the sample is:
![\mu=np=5*0.075=0.375\\\\\sigma^2=npq=5*0.075*0.925=0.347](https://tex.z-dn.net/?f=%5Cmu%3Dnp%3D5%2A0.075%3D0.375%5C%5C%5C%5C%5Csigma%5E2%3Dnpq%3D5%2A0.075%2A0.925%3D0.347)
The Chebyschev's inequality established:
![P(|X-\mu|\geq k\sigma)\leq \frac{1}{k^2}](https://tex.z-dn.net/?f=P%28%7CX-%5Cmu%7C%5Cgeq%20k%5Csigma%29%5Cleq%20%5Cfrac%7B1%7D%7Bk%5E2%7D)
Let's divide in order to simplify
![9/3 = 3](https://tex.z-dn.net/?f=9%2F3%20%3D%203)
![12/3 = 4](https://tex.z-dn.net/?f=12%2F3%20%3D%204)
We are left with 3/4. that's your simplified fraction.
The piecewise function that models the scenario is:
c(x) = $3.75*x + $5 if x < 6
c(x) = $3.25*x + $5 if x ≥ 6.
<h3>
How to write a piecewise function?</h3>
A piecewise function is a function that behaves differently in different intervals of the domain, like this one, where the cost per box changes depending on the number of box.
The function in this case, if we define x as the number of boxes bought, is:
- c(x) = $3.75*x + $5 if x < 6
- c(x) = $3.25*x + $5 if x ≥ 6.
Where the cost per box changes for x equal or larger than 6.
If you want to learn more about piecewise functions, you can read:
brainly.com/question/3628123