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?

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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 .

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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

6.5

step-by-step explanation:

you said it was in the question

~courtney

Answer from: Quest

step-by-step explanation:

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