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

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.