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vitfil [10]
2 years ago
15

Pls someone help me.

Mathematics
1 answer:
puteri [66]2 years ago
4 0

AB=EF

ABEF=ABF+AEF

NOW CONTINUES THE SOLUTION

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a statistics professor finds that when he schedules an office hour at the 10:30a, time slot, an average of three students arrive
Veseljchak [2.6K]

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

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

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.

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3 years ago
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