Y-int = 0
And the slope is 1
Answer:
5 = x
Step-by-step explanation:
5 divided by 2 = 2.5
12.5 divided by 2.5 = x = 5
Answer:
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Step-by-step explanation:
Given
![Yellow = 5\ seconds](https://tex.z-dn.net/?f=Yellow%20%3D%205%5C%20seconds)
![Green = 50\ seconds](https://tex.z-dn.net/?f=Green%20%3D%2050%5C%20seconds)
![Red = 50\ seconds](https://tex.z-dn.net/?f=Red%20%3D%2050%5C%20seconds)
Required
Determine the probability of Green or Yellow
First, we need to determine the total time
![Total = 50 + 50 + 5](https://tex.z-dn.net/?f=Total%20%3D%2050%20%2B%2050%20%2B%205)
![Total = 105\ seconds](https://tex.z-dn.net/?f=Total%20%3D%20105%5C%20seconds)
Next, is to determine the required probability
<em>This is calculated as follows:</em>
![P(Yellow\ or\ Green) = P(Yellow) + P(Green)](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20P%28Yellow%29%20%2B%20P%28Green%29)
![P(Yellow\ or\ Green) = \frac{n(Yellow)}{Total} + \frac{n(Green)}{Total}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7Bn%28Yellow%29%7D%7BTotal%7D%20%2B%20%5Cfrac%7Bn%28Green%29%7D%7BTotal%7D)
![P(Yellow\ or\ Green) = \frac{5}{105} + \frac{50}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B5%7D%7B105%7D%20%2B%20%5Cfrac%7B50%7D%7B105%7D)
![P(Yellow\ or\ Green) = \frac{5 + 50}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B5%20%2B%2050%7D%7B105%7D)
![P(Yellow\ or\ Green) = \frac{55}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B55%7D%7B105%7D)
![P(Yellow\ or\ Green) = 0.52380952381](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%200.52380952381)
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<em> -- Approximated</em>
Answer:
There is a 25.14% probability that the order will not be met during a month.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean \mu and standard deviation
, the zscore of a measure X 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)
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
.
The order will not be met if
. So we find the pvalue of Z when
, and subtract 1 by this value.
![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{6000 - 4500}{900}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B6000%20-%204500%7D%7B900%7D)
![Z = 1.67](https://tex.z-dn.net/?f=Z%20%3D%201.67)
has a pvalue of 0.7486.
So there is a 1 - 0.7486 = 0.2514 = 25.14% probability that the order will not be met during a month.