Answer:
The probability that another accident will occur that same month = 0.44907
Step-by-step explanation:
Let consider X to be the random variable that follows an exponential distribution with a mean of 52.
The mean of the exponential distribution ![\dfrac{1}{\lambda } = 52 \implies \lambda = \dfrac{1}{52}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%2052%20%5Cimplies%20%5Clambda%20%3D%20%5Cdfrac%7B1%7D%7B52%7D)
Thus, the probability distribution of X is:
![f(x) = \lambda e ^{-\lambda x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Clambda%20e%20%5E%7B-%5Clambda%20x%7D)
![f(x) =\dfrac{1}{52} e ^{-x/52} \ \ \ \ x \geq 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%5Cdfrac%7B1%7D%7B52%7D%20e%20%5E%7B-x%2F52%7D%20%20%20%20%20%5C%20%5C%20%5C%20%5C%20x%20%5Cgeq%200)
Suppose X represents the time interval between the accident that happened in October 1 and the following accident.
Then, the probability that another accident will occur in the same month is the same as the event that the time between the two accidents are less than 31 (given that the month of October have 31 days)
Thus, we can calculate the required probability as follows:
![P(X \leq 31) = \int ^{31}_{0} \ f(x) \ dx](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%20%5Cint%20%5E%7B31%7D_%7B0%7D%20%5C%20f%28x%29%20%5C%20dx)
![P(X \leq 31) = \int ^{31}_{0} \ \dfrac{1}{52} \ e^{-x/52} \ dx](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%20%5Cint%20%5E%7B31%7D_%7B0%7D%20%5C%20%5Cdfrac%7B1%7D%7B52%7D%20%5C%20e%5E%7B-x%2F52%7D%20%5C%20dx)
![P(X \leq 31) = 1 - e^{-31/52}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%201%20-%20e%5E%7B-31%2F52%7D)
![\mathbf{P(X \leq 31) = 0.44907}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28X%20%5Cleq%2031%29%20%3D%200.44907%7D)
Thus, the probability that another accident will occur that same month = 0.44907
<span>Arithmetic mean is used to describe the sum of values in a dataset divided by the number of values. It s the average of a given dataset which gives us an idea about the average value in a data set. That said, a mean of 4.3 means in the household sample (the average number of students in the data set falls within probably 4 and 4.7 probably). On the other hand,.a mean of 4.5 means there are more 8th graders than 7th graders. An increase of 0.2 from the 4.3 shows that the number of 8th graders slightly surpasses 7th graders. The principal can predict that there are more students in 8th grade because they have a higher average.</span>
Answer:
6x+42
Step-by-step explanation:
First, distribute the 8.
8x+24-2x+18.
Then, combine like terms.
6x+42
Answer:
41 and 11.
Step-by-step explanation:
Let's say the 2 numbers are x and y.
Since they add up to 52, x + y = 52.
Seeing as the difference is 30, x - y = 30 assuming x is the larger number.
We have left:
x + y = 52
x - y = 30
By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82
Therefore x = 41.
Since x + y = 52
41 + y = 52
Therefore y = 11
Therefore we have: the larger number is 41 and the smaller number is 11.
Answer:
answer is 1/16
Step-by-step explanation: