Mathematics: An eastern airport has recorded a monthly average of five near misses of landings and takeoffs in the past 5 years. We assume that the distribution of this number is Poisson. a. Find the probability that during a given month there are no near misses on landings and takeoffs at the airport. b. Find the probability that during a given month there are five near misses. c. Find the probability that there are at least five near misses during a particular month.

An eastern airport has recorded a monthly average

Ответ:

india73

02.02.2022

Mathematics

The answer to this question can be defined as follows:

In option a "0.0067".

In option b "0.1755".

In option c "0.5595".

Step-by-step explanation:

It is about the distribution of Poisson:

$\lambda = 5 (rate)$

t = 1

The formula for calculating Mean:

$\to \mu = \lambda \times t$

$\to P(X=x) = \frac{e^{-\mu} \mu^{x}}{x!}$

calculate the value of Mean:

$\to \mu =5 \times 1\\\\ \to \mu= 5$

In point a:

When the value of x is equal to 0:

$\to P(X = 0) = \frac{e^{-5} 5^{0}}{0!}$

$= \frac{e^{-5} \times 1 }{0}\\\\ = 0.0067 \times 1 \\\\ = 0.0067$

In point b:

When the value of x is equal to 5:

$\to P(X = 0) = \frac{e^{-5} 5^{5}}{5!}$

$= \frac{e^{-5} \times 3125 }{120}\\\\ = \frac{0.0067 \times 3125}{120} \\\\ = \frac{21.0560}{120}\\\\ =0.1754 \\\\$

In point c:

When the value of x is equal to 5:

$\to P(X \ge 5) = 1 - P(X < 5) \\\\ \to P(X \ge 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) \\\\ \to P(X \ge 5) = 0.5595$

0,0(0 оценок)

Ответ:

stevencardona12mejia

24.01.2021

Mathematics

2032

Step-by-step explanation:

crayon:1080

pencil:936

marker:880

calculate them:2896

18 x 48=864

2896-864=2032

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question