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?

This question is based on the probability.Therefore the answer is,(a) and (b) = .

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,

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

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

1 - P(X<5)=0.945

So,

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,

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

Therefore the answer is,(a) and (b) = .

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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

Formula :

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

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

1-P(X<5)=0.945

So,

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)=0.0607

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

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.