Using the normal distribution, it is found that there is a 0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
<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, the mean and the standard deviation are given, respectively, by:
.
The probability that on a given day, his commute will be longer than 49 minutes is <u>one subtracted by the p-value of Z when X = 49</u>, 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)
![Z = \frac{49 - 57}{4.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B49%20-%2057%7D%7B4.5%7D)
Z = -1.78
Z = -1.78 has a p-value of 0.0375.
1 - 0.0375 = 0.963.
0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
More can be learned about the normal distribution at brainly.com/question/24663213
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The volume of the rectangular pyramid is 28 cubic feet.
<h3>
How to find the volume of the pyramid?</h3>
The volume of a pyramid of base B and height H is given by:
![V = (1/3)*B*H](https://tex.z-dn.net/?f=V%20%3D%20%281%2F3%29%2AB%2AH)
Here we know that the height is H = 7ft, and the base is a rectangle of 4ft by 3ft, so the area of the base is:
![B = 4ft*3t = 12ft^2](https://tex.z-dn.net/?f=B%20%3D%204ft%2A3t%20%3D%2012ft%5E2)
Then the volume of the pyramid is:
![V = (1/3)*7ft*12ft^2 = 28ft^3](https://tex.z-dn.net/?f=V%20%3D%20%281%2F3%29%2A7ft%2A12ft%5E2%20%3D%2028ft%5E3)
If you want to learn more about volumes:
brainly.com/question/1972490
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I think A, but I'm not sure as what's the question?