Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
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:
- The sample has 20 pills, hence
.
- 100 - 4 = 96% are acceptable, hence
![p = 0.96](https://tex.z-dn.net/?f=p%20%3D%200.96)
The probability that <u>fewer that 5 in a sample of 20 pills</u> will be acceptable is:
![P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)](https://tex.z-dn.net/?f=P%28X%20%3C%205%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%2B%20P%28X%20%3D%204%29)
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 = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B20%2C0%7D.%280.96%29%5E%7B0%7D.%280.04%29%5E%7B20%7D%20%3D%200)
![P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B20%2C1%7D.%280.96%29%5E%7B1%7D.%280.04%29%5E%7B19%7D%20%3D%200)
![P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B20%2C2%7D.%280.96%29%5E%7B2%7D.%280.04%29%5E%7B18%7D%20%3D%200)
![P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B20%2C3%7D.%280.96%29%5E%7B3%7D.%280.04%29%5E%7B17%7D%20%3D%200)
![P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B20%2C4%7D.%280.96%29%5E%7B4%7D.%280.04%29%5E%7B16%7D%20%3D%200)
0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
A similar problem is given at brainly.com/question/24863377
Answer:
452+(783-546)
Step-by-step explanation:
Add 452 ; 452+
the difference of 783 and 546 ; 783-546
You add in the parentheses so that you're adding 452 to the difference of the two other numbers instead of to 783.
Answer:
24
Step-by-step explanation:
you would multiply 3 tables by 4 students, that would be twelve. then 12 times 2, which is 24. Or you could find the pencils by multiplying 2 with 8 and then multiplying by 3. :)
Answer:
C
Step-by-step explanation:
because vertical angles angles that are opposite each other and formed by two intersecting lines are congruent
hope this helps :D
<h2>
Hello!</h2>
The answer is:
The correct option is
a) ![Resultant=\sqrt{22^{2} +4^{2} }](https://tex.z-dn.net/?f=Resultant%3D%5Csqrt%7B22%5E%7B2%7D%20%2B4%5E%7B2%7D%20%7D)
<h2>
Why?</h2>
Since a right triangle is formed, we can calculate the resultant force using the Pythagorean Theorem which states that:
![c=\sqrt{a^{2}+b^{2}}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D)
Where,
c, is the hypothenuse.
a, is one triangle leg.
b, is the other triangle leg.
So, we are given the information:
![a=22mph](https://tex.z-dn.net/?f=a%3D22mph)
![b=4mph](https://tex.z-dn.net/?f=b%3D4mph)
So, calculating the resultant force (hypothenuse), we have:
![Resultant=\sqrt{22^{2} +4^{2} }](https://tex.z-dn.net/?f=Resultant%3D%5Csqrt%7B22%5E%7B2%7D%20%2B4%5E%7B2%7D%20%7D)
Hence, the expression that would find the result velocity is:
a) [tex]Resultant=\sqrt{22^{2} +4^{2} }[/tex]
Have a nice day!