Answer:
![P(X=8) = 0.0194](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%200.0194)
![P(X \ge 8)= 0.9820](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29%3D%200.9820)
![P(X \ge 1)= 1](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%3D%201)
![P(X\le 1) = 0.0000049](https://tex.z-dn.net/?f=P%28X%5Cle%201%29%20%3D%200.0000049)
Step-by-step explanation:
Given
![\lambda = 15](https://tex.z-dn.net/?f=%5Clambda%20%3D%2015)
Poisson distribution is given by:
![P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cfrac%7B%5Clambda%5Ex%20e%5E%7B-%5Clambda%7D%7D%7Bx%21%7D)
Solving (a): 8 bugs
This implies that:
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
So, we have:
![P(X=8) = \frac{15^8 * e^{-15}}{8!}](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%20%5Cfrac%7B15%5E8%20%2A%20e%5E%7B-15%7D%7D%7B8%21%7D)
![P(X=8) = \frac{783.99418938}{40320}](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%20%5Cfrac%7B783.99418938%7D%7B40320%7D)
![P(X=8) = 0.0194](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%200.0194)
Solving (b): At least 8 bugs
This is represented as: ![P(X \ge 8)](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29)
Using complement rule:
![P(X \ge 8)= 1 - P(X](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29%3D%201%20-%20P%28X%3C8%29)
Where
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%20P%28X%3D1%29%20%2B%20P%28X%3D2%29%20%2B%20P%28X%3D3%29%20%2B%20P%28X%3D4%29%20%2B%20P%28X%3D5%29%20%2B%20P%28X%3D6%29%20%2B%20P%28X%3D7%29)
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%20%5Cfrac%7B15%5E1%20%2A%20e%5E%7B-15%7D%7D%7B1%21%7D%20%2B%20%5Cfrac%7B15%5E2%20%2A%20e%5E%7B-15%7D%7D%7B2%21%7D%20%2B%20%5Cfrac%7B15%5E3%20%2A%20e%5E%7B-15%7D%7D%7B3%21%7D%20%2B%20%5Cfrac%7B15%5E4%20%2A%20e%5E%7B-15%7D%7D%7B4%21%7D%20%2B%20%5Cfrac%7B15%5E5%20%2A%20e%5E%7B-15%7D%7D%7B5%21%7D%20%2B%20%5Cfrac%7B15%5E6%20%2A%20e%5E%7B-15%7D%7D%7B6%21%7D%20%2B%20%5Cfrac%7B15%5E7%20%2A%20e%5E%7B-15%7D%7D%7B7%21%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%20%28%5Cfrac%7B15%5E1%7D%7B1%21%7D%20%2B%20%5Cfrac%7B15%5E2%7D%7B2%21%7D%20%2B%20%5Cfrac%7B15%5E3%20%7D%7B3%21%7D%20%2B%20%5Cfrac%7B15%5E4%7D%7B4%21%7D%20%2B%20%5Cfrac%7B15%5E5%7D%7B5%21%7D%20%2B%20%5Cfrac%7B15%5E6%7D%7B6%21%7D%20%2B%20%5Cfrac%7B15%5E7%7D%7B7%21%7D%29%20e%5E%7B-15%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%20%2815%20%2B%20112.5%20%2B%20562.5%20%2B%202109.375%20%2B%206328.125%20%2B%2015820.3125%20%2B%2033900.6696429%29%20%2Ae%5E%7B-15%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%2058848.4821429%20%2Ae%5E%7B-15%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C8%29%20%3D%200.0180)
So:
![P(X \ge 8)= 1 - P(X](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29%3D%201%20-%20P%28X%3C8%29)
![P(X \ge 8)= 1 - 0.0180](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29%3D%201%20-%200.0180)
![P(X \ge 8)= 0.9820](https://tex.z-dn.net/?f=P%28X%20%5Cge%208%29%3D%200.9820)
Solving (c): At least 1
This is represented as: ![P(X \ge 1)](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29)
Using complement rule:
![P(X \ge 1)= 1 - P(X](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%3D%201%20-%20P%28X%3C1%29)
![P(X](https://tex.z-dn.net/?f=P%28X%3C1%29%20%3D%20P%28X%20%3D%200%29)
![P(X](https://tex.z-dn.net/?f=P%28X%3C1%29%20%3D%20%5Cfrac%7B15%5E0%20e%5E%7B-15%7D%7D%7B0%21%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C1%29%20%3D%20%5Cfrac%7Be%5E%7B-15%7D%7D%7B1%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C1%29%20%3D%20e%5E%7B-15%7D)
So:
![P(X \ge 1)= 1 - P(X](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%3D%201%20-%20P%28X%3C1%29)
![P(X \ge 1)= 1 - e^{-15](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%3D%201%20-%20e%5E%7B-15)
![P(X \ge 1)= 1](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%3D%201)
Solving (d): Not more than 1
This implies at most 1.
It is represented as:
![P(X\le 1)](https://tex.z-dn.net/?f=P%28X%5Cle%201%29)
It is calculated using:
![P(X\le 1) = P(X = 0) + P(X =1)](https://tex.z-dn.net/?f=P%28X%5Cle%201%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D1%29)
![P(X = 0) = e^{-15}](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20e%5E%7B-15%7D)
![P(X=1) = \frac{15^1 * e^{-15}}{1!}](https://tex.z-dn.net/?f=P%28X%3D1%29%20%3D%20%5Cfrac%7B15%5E1%20%2A%20e%5E%7B-15%7D%7D%7B1%21%7D)
![P(X=1) = 15 * e^{-15}](https://tex.z-dn.net/?f=P%28X%3D1%29%20%3D%2015%20%2A%20e%5E%7B-15%7D)
So:
![P(X\le 1) = e^{-15} + 15 * e^{-15}](https://tex.z-dn.net/?f=P%28X%5Cle%201%29%20%3D%20e%5E%7B-15%7D%20%2B%2015%20%2A%20e%5E%7B-15%7D)
![P(X\le 1) = 0.00000489443](https://tex.z-dn.net/?f=P%28X%5Cle%201%29%20%3D%200.00000489443)
![P(X\le 1) = 0.0000049](https://tex.z-dn.net/?f=P%28X%5Cle%201%29%20%3D%200.0000049)
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is
Step-by-step explanation:
From the question we told that
The test statistics is ![t = 0.72](https://tex.z-dn.net/?f=t%20%3D%20%200.72)
The number of student is n = 5
The degree of freedom can be mathematically evaluated as
![D = n- 1](https://tex.z-dn.net/?f=D%20%3D%20%20n-%201)
=> ![D = 5- 1 = 4](https://tex.z-dn.net/?f=D%20%3D%20%205-%201%20%3D%20%204)
The p-value is mathematically evaluated as
![p-value = p(T \le - |-0.72|)](https://tex.z-dn.net/?f=p-value%20%3D%20%20p%28T%20%5Cle%20-%20%7C-0.72%7C%29)
using the z table(shown in second and third image ) we obtain that
![p-value = 0.2557](https://tex.z-dn.net/?f=p-value%20%3D%20%200.2557)
Answer:
The limit of a sum is equal to the sum of the limits.
Step-by-step explanation:
The limits of a constant times a function is equal to the constant times the limit of the function.
Answer:
Step-by-step explanation:
By Geometric mean property:
![BD = \sqrt{3 \times 7} \\ BD = \sqrt{21} \\ by \: pythagoras \: theorem \\ {x}^{2} = { (\sqrt{21}) }^{2} + {(3)}^{2} \\ {x}^{2} = 21 + 9 \\ {x}^{2} = 30 \\ x = \sqrt{30}](https://tex.z-dn.net/?f=BD%20%3D%20%20%5Csqrt%7B3%20%5Ctimes%207%7D%20%20%5C%5C%20BD%20%3D%20%20%5Csqrt%7B21%7D%20%5C%5C%20by%20%5C%3A%20pythagoras%20%5C%3A%20theorem%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20%7B%20%28%5Csqrt%7B21%7D%29%20%7D%5E%7B2%7D%20%20%2B%20%20%7B%283%29%7D%5E%7B2%7D%20%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%2021%20%2B%209%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%2030%20%5C%5C%20x%20%3D%20%20%5Csqrt%7B30%7D%20)
Answer:
correct amswer Fh id 19 sir