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Mathematics, 02.10.2019 04:20 ntrann22

The number of messages that arrive at a web site is a poisson distributed random variable with a mean of 6 messages per hour. round your answers to four decimal places (e. g. 98.7654). (a) what is the probability that 5 messages are received in 1 hour? (b) what is the probability that 10 messages are received in 1.5 hours? (c) what is the probability that less than 2 messages are received in 1/2 hour?

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Answer from: blondie02

a) There is a 16.0623% probability that 5 messages are received in 1 hour.

b) There is a 11.5880% probability that 10 messages are received in 1.5 hours.

c) There is a 22.4042% probability that 2 messages are received in 0.5 hours.

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.

In this problem, we have a mean of 6 messages per hour.

(a) What is the probability that 5 messages are received in 1 hour?

Find the value of P when x = 5 and $\mu = 6$

So

$P(X = 5) = \frac{e^{-6}*(6)^{5}}{(5)!} = 0.160623$

There is a 16.0623% probability that 5 messages are received in 1 hour.

(b) What is the probability that 10 messages are received in 1.5 hours?

The mean is 6 messages in one hour.

For 1.5 hours, the mean is 6*1.5 = 9 messages.

So

We have to find the value of P when x = 10 and $\mu = 9$ .

$P(X = 10) = \frac{e^{-9}*(9)^{10}}{(10)!} = 0.115880$

There is a 11.5880% probability that 10 messages are received in 1.5 hours.

(c) What is the probability that less than 2 messages are received in 1/2 hour?

The mean is 6 messages in one hour.

For 0.5 hours, the mean is 6*0.5 = 3 messages.

So

We have to find the value of P when x = 2 and $\mu = 3$ .

$P(X = 10) = \frac{e^{-3}*(3)^{2}}{(2)!} = 0.224042$

There is a 22.4042% probability that 2 messages are received in 0.5 hours.

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Answer from: Quest

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

ansver

Answer from: Quest

The answer is 10. and if you go by pemdas you would 1. multiplication 2. division 3. addition 4. subtraction
Solve the following problem using the order of operations. then match each operation with its place

Solve the following problem using the order of operations. then match each operation with its place

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