Answer:
i)
ii)
And replacing we got:
![P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.00317%2B0.0211%2B0.0669%5D%3D%200.90883)
iii) ![P(X](https://tex.z-dn.net/?f=P%28X%20%3C2%29%3D%200.00317%2B%200.0211%3D%200.02427)
Step-by-step explanation:
Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part i
We want this probability:
Part ii
We want this probability:
And we can use the complement rule and we have:
![P(X\geq 3) = 1-P(X](https://tex.z-dn.net/?f=P%28X%5Cgeq%203%29%20%3D%201-P%28X%3C3%29%3D%201-P%28X%20%5Cleq%202%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%20%2BP%28X%3D2%29%5D)
And if we find the individual probabilites we got:
And replacing we got:
![P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.00317%2B0.0211%2B0.0669%5D%3D%200.90883)
Part iii
We want this probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%20%3C2%29%3D%20P%28X%3D0%29%20%2BP%28X%3D1%29)
And replacing we got:
![P(X](https://tex.z-dn.net/?f=P%28X%20%3C2%29%3D%200.00317%2B%200.0211%3D%200.02427)