Mathematics, 27.03.2020 01:46 kylabreanne120

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of six per hour. (a) What is the probability that exactly two arrivals occur during a particular hour? (Round your answer to three decimal places.) (b) What is the probability that at least two people arrive during a particular hour? (Round your answer to three decimal places.) (c) How many people do you expect to arrive during a 45-min period? people

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Answer from: edjiejwi

a) 0.045 = 4.5% probability that exactly two arrivals occur during a particular hour

b) 0.983 = 98.3% probability that at least two people arrive during a particular hour

c) 4.5 arrivals during a 45-min period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Poisson process with a rate parameter of six per hour.

This means that $\mu = 6$ . So

(a) What is the probability that exactly two arrivals occur during a particular hour?

This is P(X = 2).

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

$P(X = 2) = \frac{e^{-6}*(6)^{2}}{(2)!} = 0.045$

0.045 = 4.5% probability that exactly two arrivals occur during a particular hour

(b) What is the probability that at least two people arrive during a particular hour?

Either less than two people arrive during a particular hour, or at least two do. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$

$P(X \geq 2) = 1 - P(X < 2)$

In which

P(X < 2) = P(X = 0) + P(X = 1)

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

$P(X = 0) = \frac{e^{-6}*(6)^{0}}{(0)!} = 0.002$

$P(X = 1) = \frac{e^{-6}*(6)^{1}}{(1)!} = 0.015$

P(X < 2) = P(X = 0) + P(X = 1) = 0.002 + 0.015 = 0.017

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.017 = 0.983$

0.983 = 98.3% probability that at least two people arrive during a particular hour

An hour has 60 mins.

45/60 = 3/4.

$\mu = \frac{3*6}{4} = 4.5$

4.5 arrivals during a 45-min period.

Answer from: Quest

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

Answer from: Quest

answer:

total cost for tiles and paints is $924.

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

$\text{area of walls and ceiling}=(2*40*15)+(2*3*15)+(40*3)$

$\text{area of walls and ceiling}=1200+90+120$

$\text{area of walls and ceiling}=1410$

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

$\text{ the total painting cost}=10*(\frac{1410}{25})$

$\text{ the total painting cost}=10*56.4=564$

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

$\text{area of floor} = 40*3\text{ square meters}$

$\text{area of floor} =120\text{ square meters}$

given: 1m squared floor tiles costs $3. so,

$\text{total cost for tiles} = 3*120 = 360$

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

$\text{combined total cost}= 564+360 = 924$

therefore, the combined total cost of tiles and paint is $924.

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The number of people arriving for treatment at an emergency room can be modeled by a Poisson process...