Answer:
75.76% probability that there will be 10 or more customers at this bank in one hour.
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.
A bank gets an average of 12 customers per hour.
This means that ![\mu = 12](https://tex.z-dn.net/?f=%5Cmu%20%3D%2012)
Find the probability that there will be 10 or more customers at this bank in one hour.
Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then
![P(X < 10) + P(X \geq 10) = 1](https://tex.z-dn.net/?f=P%28X%20%3C%2010%29%20%2B%20P%28X%20%5Cgeq%2010%29%20%3D%201)
We want ![P(X \geq 10)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2010%29)
Then
![P(X \geq 10) = 1 - P(X < 10)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2010%29%20%3D%201%20-%20P%28X%20%3C%2010%29)
In which
![P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)](https://tex.z-dn.net/?f=P%28X%20%3C%2010%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%2B%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29%20%2B%20P%28X%20%3D%206%29%20%2B%20P%28X%20%3D%207%29%20%2B%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29)
So
![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^{-12}*12^{0}}{(0)!} \approx 0](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B0%7D%7D%7B%280%29%21%7D%20%5Capprox%200)
![P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.0001)
![P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.0004)
![P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B3%7D%7D%7B%283%29%21%7D%20%3D%200.0018)
![P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B4%7D%7D%7B%284%29%21%7D%20%3D%200.0053)
![P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B5%7D%7D%7B%285%29%21%7D%20%3D%200.0127)
![P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255](https://tex.z-dn.net/?f=P%28X%20%3D%206%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B6%7D%7D%7B%286%29%21%7D%20%3D%200.0255)
![P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437](https://tex.z-dn.net/?f=P%28X%20%3D%207%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B7%7D%7D%7B%287%29%21%7D%20%3D%200.0437)
![P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B8%7D%7D%7B%288%29%21%7D%20%3D%200.0655)
![P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20%5Cfrac%7Be%5E%7B-12%7D%2A12%5E%7B9%7D%7D%7B%289%29%21%7D%20%3D%200.0874)
![P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424](https://tex.z-dn.net/?f=P%28X%20%3C%2010%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%2B%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29%20%2B%20P%28X%20%3D%206%29%20%2B%20P%28X%20%3D%207%29%20%2B%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29%20%3D%200%20%2B%200.0001%20%2B%200.0004%20%2B%200.0018%20%2B%200.0053%20%2B%200.0127%20%2B%200.0255%20%2B%200.0437%20%2B%200.0655%20%2B%200.0874%20%3D%200.2424)
Then
![P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2010%29%20%3D%201%20-%20P%28X%20%3C%2010%29%20%3D%201%20-%200.2424%20%3D%200.7576)
75.76% probability that there will be 10 or more customers at this bank in one hour.
1. Would be 60% like how 1/100 equals 1%
2. Excel conditional formatting is a really powerful feature when it
comes to applying different formats to data that meets certain
conditions. It can help you highlight the most important information in
your spreadsheets and identify variances of cells' values with a quick
glance.
The first 4 terms are 2, 2/3, 2/9, and 2/27
I hope this was helpful, i haven't done sequences in a while
Answer:
your anserw is 1,300
Step-by-step explanation:
please rate me the branlest
Answer:
D
Step-by-step explanation:
I am pretty sure it is D because the numbers on the chart don't seem inconsistent. You go from 11 to 2 which would give a big drop so it wouldn't be a linear function.