<h3>
Answer: 98 inches</h3>
Work Shown:
3 1/2 inches = 3.5 inches
total width = 28*3.5 = 98 inches
Answer:
125 = 5 * 5 * 5 = 5^3
Step-by-step explanation:
125 is equal to 5 times 5 times 5, and a power is a way to write repeated multiplication, just by saying what number it is and the putting a ^ sign and then saying how many times there is that number. There is 5 three times, so the power is 5^3.
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
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23.99 multiplied by .44, you'll get the product of that. Take that product and subtract it from 23.99 and you'll get your answer
23.99 x .44 = 10.5556
23.99 - 10.5556 = 13.43 <span />