Answer:
0.5,0.25,3/8,1 1/4
Step-by-step explanation:
Answer:
4 and 6.
Step-by-step explanation:
There are 4 different grades represented, so for the first question, there are 4 ways that the students can sit if they must sit together by grade.
For the second question, there are 3 grades other than senior level, so it starts with 3 ways that the students can be seated. 3 ways x 2 students per way = 6 ways
Answer:
The endpoints of the line segment CD are:
$$C=(x_1,y_1)= (-4, 8) \\ D= (x_2,y_2)= (8, -4) $$
We find the midpoint using th
Answer:
The last answer choice.
Step-by-step explanation:
8/10 is equal to 0.80, so that's the answer! Hope it helps!
The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
<h3>How to determine the probability?</h3>
The given parameters are:
- Sample size, n = 100
- Population proportion, p = 82%
Start by calculating the mean:
![\mu = np](https://tex.z-dn.net/?f=%5Cmu%20%3D%20np)
![\mu = 100 * 82\%](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100%20%2A%2082%5C%25)
![\mu = 82](https://tex.z-dn.net/?f=%5Cmu%20%3D%2082)
Calculate the standard deviation:
![\sigma = \sqrt{\mu(1 - p)](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cmu%281%20-%20p%29)
![\sigma = \sqrt{82 * (1 - 82\%)](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B82%20%2A%20%281%20-%2082%5C%25%29)
![\sigma = 3.84](https://tex.z-dn.net/?f=%5Csigma%20%3D%203.84)
Within ± 0.02 of the population proportion are:
![x_{min} = 82 * (1 - 0.02) = 80.38](https://tex.z-dn.net/?f=x_%7Bmin%7D%20%3D%2082%20%2A%20%281%20-%200.02%29%20%3D%2080.38)
![x_{max} = 82 * (1 + 0.02) = 83.64](https://tex.z-dn.net/?f=x_%7Bmax%7D%20%3D%2082%20%2A%20%281%20%2B%200.02%29%20%3D%2083.64)
Calculate the z-scores at these points using:
![z = \frac{x - \mu}{\sigma}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7Bx%20-%20%5Cmu%7D%7B%5Csigma%7D)
So, we have:
![z_1 = \frac{80.36 - 82}{3.84} = -0.43](https://tex.z-dn.net/?f=z_1%20%3D%20%5Cfrac%7B80.36%20-%2082%7D%7B3.84%7D%20%3D%20-0.43)
![z_2 = \frac{83.64 - 82}{3.84} = 0.43](https://tex.z-dn.net/?f=z_2%20%3D%20%5Cfrac%7B83.64%20-%2082%7D%7B3.84%7D%20%3D%200.43)
The probability is then represented as:
P(x ± 0.02) = P(-0.43 < z < 0.43)
Using the z table of probabilities, we have:
P(x ± 0.02) = 0.3328
Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
Read more about probability at:
brainly.com/question/25870256
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