Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so ![\mu = 2*3 = 6](https://tex.z-dn.net/?f=%5Cmu%20%3D%202%2A3%20%3D%206)
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
![P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)](https://tex.z-dn.net/?f=P%28X%20%3C%204%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29)
In which
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.0025)
![P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.0149)
![P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.0446)
![P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B3%7D%7D%7B%283%29%21%7D%20%3D%200.0892)
Then
![P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512](https://tex.z-dn.net/?f=P%28X%20%3C%204%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%3D%200.0025%20%2B%200.0149%20%2B%200.0446%20%2B%200.0892%20%3D%200.1512)
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Answer:
3 hours 39 minutes
Step-by-step explanation:
6 to 10 = 4 hours
35 to 14 = -21
4 x 60 = 240
240 - 21 = 219
220 to hours and minutes = 3 hours and 39 minutes
If my answer is incorrect, pls correct me!
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-Chetan K
Answer:
Option B. Quadratic
Step-by-step explanation:
In a regression model, the value of
tells us how accurately the model fits the data.
That closer the value of
of 1 is, better is the model.
This can be used to compare what type of model is most convenient to use in some cases.
In this problem the attached table shows a comparison of the value of
for 3 models
Linear
Quadratic
Exponential
Note that the value of
that is closest to 1 is that which corresponds to the quadratic model.
![r ^ 2 = 0.89](https://tex.z-dn.net/?f=r%20%5E%202%20%3D%200.89)
Therefore the function that best fits the points is the quadratic
Answer:
Step-by-step explanation:
C
Answer:
p = 0.68 and p^ = 0.6
Step-by-step explanation:
Jackie received 68% of the votes in an election.
Here p is the decimal equivalent of 68 %.Hence ,
p = 0.68
Now we have taken a sample of 30 people from the total number of voters and we have to find the percentage of votes that Jackie gets in this .
Out of 30 people Jackie got 18 votes. Hence,
p^ =
= 0.6
Hence the values are
p = 0.68 and p^ = 0.6
In the random sample we have taken the probability of Jackie has decreased but it will be compensated by another sample where it will be more.