Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
The probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.
Step-by-step explanation:
Let <em>X</em> = number of students arriving at the 10:30 AM time slot.
The average number of students arriving at the 10:30 AM time slot is, <em>λ</em> = 3.
A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables. For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.
The random variable <em>X</em> is also a Poisson random variable because it represents the fixed number of students arriving at the 10:30 AM time slot.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 3.
The probability mass function of <em>X</em> is given by:
![P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...,\ \lambda>0](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5Cfrac%7Be%5E%7B-%5Clambda%7D%5Clambda%5E%7Bx%7D%7D%7Bx%21%7D%3B%5C%20x%3D0%2C1%2C2%2C3...%2C%5C%20%5Clambda%3E0)
Compute the probability of <em>X</em> = 2 as follows:
![P(X=2)=\frac{e^{-3}3^{2}}{2!}=\frac{0.0498\times 9}{2}=0.2241](https://tex.z-dn.net/?f=P%28X%3D2%29%3D%5Cfrac%7Be%5E%7B-3%7D3%5E%7B2%7D%7D%7B2%21%7D%3D%5Cfrac%7B0.0498%5Ctimes%209%7D%7B2%7D%3D0.2241)
Thus, the probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.