32 + 20 = 52 = 4(8+5) = 4(13)
18 + 27 = 45 = 9(2+3) = 9(5)
Using the normal distribution, it is found that the mean is of
and the standard deviation is of
.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the p-value of Z when X = 30 is of 0.1, hence, when X = 30, Z = -1.28, so:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.28 = \frac{30 - \mu}{\sigma}](https://tex.z-dn.net/?f=-1.28%20%3D%20%5Cfrac%7B30%20-%20%5Cmu%7D%7B%5Csigma%7D)
![30 - \mu = -1.28\sigma](https://tex.z-dn.net/?f=30%20-%20%5Cmu%20%3D%20-1.28%5Csigma)
![\mu = 30 + 1.28\sigma](https://tex.z-dn.net/?f=%5Cmu%20%3D%2030%20%2B%201.28%5Csigma)
The p-value of Z when X = 32.5 is of 0.2, hence when X = 32.5, Z = -0.84, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-0.84 = \frac{32.5 - \mu}{\sigma}](https://tex.z-dn.net/?f=-0.84%20%3D%20%5Cfrac%7B32.5%20-%20%5Cmu%7D%7B%5Csigma%7D)
![32.5 - \mu = -0.84\sigma](https://tex.z-dn.net/?f=32.5%20-%20%5Cmu%20%3D%20-0.84%5Csigma)
![\mu = 32.5 + 0.84\sigma](https://tex.z-dn.net/?f=%5Cmu%20%3D%2032.5%20%2B%200.84%5Csigma)
Hence:
![30 + 1.28\sigma = 32.5 + 0.84\sigma](https://tex.z-dn.net/?f=30%20%2B%201.28%5Csigma%20%3D%2032.5%20%2B%200.84%5Csigma)
![0.44\sigma = 2.5](https://tex.z-dn.net/?f=0.44%5Csigma%20%3D%202.5)
![\sigma = \frac{2.5}{0.44}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cfrac%7B2.5%7D%7B0.44%7D)
![\sigma = 5.68](https://tex.z-dn.net/?f=%5Csigma%20%3D%205.68)
![\mu = 32.5 + 0.84(5.68) = 37.27](https://tex.z-dn.net/?f=%5Cmu%20%3D%2032.5%20%2B%200.84%285.68%29%20%3D%2037.27)
More can be learned about the normal distribution at brainly.com/question/27643290
#SPJ1
5x5+5x2 and I think that is a good way to explain this
Answer:
4
Step-by-step explanation:
![gradient = \frac{y2 - y1}{x2 - x1}](https://tex.z-dn.net/?f=gradient%20%3D%20%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20)
![y2 = - 3 \\ y1 = 3 \\ x2 = 2 \\ x1 = 3](https://tex.z-dn.net/?f=y2%20%3D%20%20-%203%20%5C%5C%20y1%20%3D%203%20%5C%5C%20x2%20%3D%202%20%5C%5C%20x1%20%3D%203)
![\frac{ - 3 - 1}{2 - 3} = \frac{ - 4}{ - 1} = 4](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%203%20-%201%7D%7B2%20-%203%7D%20%20%3D%20%20%5Cfrac%7B%20-%204%7D%7B%20-%20%201%7D%20%20%3D%204)
Answer:
Therefore, the constant multiple of liters in jug to the weight in kilogram is 0.62(approx)
Step-by-step explanation:
Given, Madison is carrying a 11.3 liter jug of sport drink that weights 7 kg.
Let the constant term be x
According to the problem,
11.3 × x = 7
⇔![x =\frac{7}{11.3}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B7%7D%7B11.3%7D)
⇔x = 0.62
Therefore, the constant multiple of liters in jug to the weight in kilogram is 0.62(approx)