Mathematics, 16.03.2020 20:08 breemills9552

Messages arrive at an electronic message center at random times, with an average of 9 messages per hour. (a) What is the probability of receiving at least five messages during the next hour? (b) What is the probability of receiving exactly five messages during the next hour?

Answers: 1

Show answers

Answers

Answer from: MileenaKitana

This question is based on the probability.Therefore the answer is,(a) $P(X\geq 5) = 0.945$ and (b) = P(X=5) = 0.0607 .

Given:

Messages arrive at an electronic message center at random times, with an average of 9 messages per hour.

According to the question,

Now, X follows the poison distribution with,

$P(X=x) = \dfrac{e^{- \lambda } \lambda^x}{x!}$

a) We need to find the probability of receiving at least five messages during the next hour i.e.

$P(X\geq 5) = 1 - P(X$

1 - P(X<5) = 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

1-P(X

1 - P(X<5)=0.945

So, $P(X\geq 5) = 0.945$

Thus, The probability of receiving at least five messages during the next hour is 0.945.

(b) Now, find he probability of receiving exactly five messages during the next hour is,

$P(X=5) = \dfrac{e^{- 9} 9^5}{5!}\\P(X=5) = 0.0607$

Thus, the probability of receiving exactly five messages during the next hour is 0.0607.

Therefore the answer is,(a) $P(X\geq 5) = 0.945$ and (b) = P(X=5) = 0.0607 .

For more details, prefer this link:

link

Answer from: zandariouslee

The probability of receiving at least five messages during the next hour is 0.945

The probability of receiving exactly five messages during the next hour is 0.0607

Step-by-step explanation:

We are given that Messages arrive at an electronic message center at random times, with an average of 9 messages per hour.

X follows poisson distribution with $\lambda = 9$

Formula : $P(X=x)=\frac{e^{-\lambda} \lambda^x}{x!}$

a) We are supposed to find the probability of receiving at least five messages during the next hour i.e. $P(X\geq 5)=1-P(X$

1-P(X<5)=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

1-P(X

1-P(X<5)=0.945

So, $P(X\geq 5)=0.945$

So, The probability of receiving at least five messages during the next hour is 0.945

(b) What is the probability of receiving exactly five messages during the next hour?

$P(X=5)=\frac{e^{-9} 9^5}{5!}$

P(X=5)=0.0607

Hence the probability of receiving exactly five messages during the next hour is 0.0607

Answer from: Quest

the answer is 31.27mph

Answer from: Quest

kjgfcvbjkl

step-by-step explanation:

sdfghjkl; vbnm,

Another question on Mathematics

Mathematics, 21.06.2019 18:40

That table shows measurements (in invhes$ from cubes with different side lengths. which pairs of variables have a linear relationship? check all that apply

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Mat bought a phone for $100. he has to pay $30 per mouth. if he has paid $640 in total, how many mouth has he had the phone?

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Which spreadsheet would be used to compute the first nine terms of the geometric sequence a^n=32•(1/2)n-1

Answers: 3

Answer

Mathematics, 22.06.2019 00:30

Which polynomial equation of least degree has -2, -2, 3, and 3 as four of its roots? (x + 2)(x - 3) = 0 (x - 2)-2(x + 3)3 = 0 (x-2 + 2)(x2- 3) = 0 (x + 2)2(x - 3)2 = 0

Answers: 2

Answer

You know the right answer?

Messages arrive at an electronic message center at random times, with an average of 9 messages per h...

Questions