Answer:
(a) The probability of the event (<em>X</em> > 84) is 0.007.
(b) The probability of the event (<em>X</em> < 64) is 0.483.
Step-by-step explanation:
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 64.
The probability mass function of a Poisson distribution is:

(a)
Compute the probability of the event (<em>X</em> > 84) as follows:
P (X > 84) = 1 - P (X ≤ 84)
![=1-\sum _{x=0}^{x=84}\frac{e^{-64}(64)^{x}}{x!}\\=1-[e^{-64}\sum _{x=0}^{x=84}\frac{(64)^{x}}{x!}]\\=1-[e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{84}}{84!}]]\\=1-0.99308\\=0.00692\\\approx0.007](https://tex.z-dn.net/?f=%3D1-%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D84%7D%5Cfrac%7Be%5E%7B-64%7D%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3D1-%5Be%5E%7B-64%7D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D84%7D%5Cfrac%7B%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5D%5C%5C%3D1-%5Be%5E%7B-64%7D%5B%5Cfrac%7B%2864%29%5E%7B0%7D%7D%7B0%21%7D%2B%5Cfrac%7B%2864%29%5E%7B1%7D%7D%7B1%21%7D%2B%5Cfrac%7B%2864%29%5E%7B2%7D%7D%7B2%21%7D%2B...%2B%5Cfrac%7B%2864%29%5E%7B84%7D%7D%7B84%21%7D%5D%5D%5C%5C%3D1-0.99308%5C%5C%3D0.00692%5C%5C%5Capprox0.007)
Thus, the probability of the event (<em>X</em> > 84) is 0.007.
(b)
Compute the probability of the event (<em>X</em> < 64) as follows:
P (X < 64) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 63)
![=\sum _{x=0}^{x=63}\frac{e^{-64}(64)^{x}}{x!}\\=e^{-64}\sum _{x=0}^{x=63}\frac{(64)^{x}}{x!}\\=e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{63}}{63!}]\\=0.48338\\\approx0.483](https://tex.z-dn.net/?f=%3D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D63%7D%5Cfrac%7Be%5E%7B-64%7D%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3De%5E%7B-64%7D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D63%7D%5Cfrac%7B%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3De%5E%7B-64%7D%5B%5Cfrac%7B%2864%29%5E%7B0%7D%7D%7B0%21%7D%2B%5Cfrac%7B%2864%29%5E%7B1%7D%7D%7B1%21%7D%2B%5Cfrac%7B%2864%29%5E%7B2%7D%7D%7B2%21%7D%2B...%2B%5Cfrac%7B%2864%29%5E%7B63%7D%7D%7B63%21%7D%5D%5C%5C%3D0.48338%5C%5C%5Capprox0.483)
Thus, the probability of the event (<em>X</em> < 64) is 0.483.
Answer:
I
Step-by-step explanation:
At least means greater than or equal to
a ≥ 10
That is a closed circle
We have a closed circle at 10
We have to be at least 10 years old
Closed circle at 10, line going to the right
If width is equal to length then it's a square.
perimeter in this case would be 4x length of each side.
that is( 4 x length)= 210.5
length= width= 210.5/4= 52.62 feet