A reservation service employs six information operators who receive requests for information independently of one another, each according to a Poisson process with rate ???? = 2 per minute. a. What is the probability that during a given 1 min period, the first operator receives no requests? (Round your answer to three decimal places.) b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests? (Round your answer to five decimal places.)

Answers

Answer 1
Answer:

Answer:

a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution.

Poisson distribution:

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) = (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.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)

In which C_(n,x) is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_(n,x) = (n!)/(x!(n-x)!)

And p is the probability of X happening.

Poisson process with rate 2 per minute

This means that \mu = 2

a. What is the probability that during a given 1 min period, the first operator receives no requests?

Single operator, so we use the Poisson distribution.

This is P(X = 0).

P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)

P(X = 0) = (e^(-2)*2^(0))/((0)!) = 0.135

0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?

6 operators, so we use the binomial distribution with n = 6

Each operator has a 13.5% probability of receiving no requests during a minute, so p = 0.135

This is P(X = 3).

P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)

P(X = 3) = C_(6,3).(0.135)^(3).(0.865)^(3) = 0.03185

0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests


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A)3 hours
B)3.5 hours
C)4 hours
D)4.5 hours
PLS ANSWER

Answers

Answer:

D)4.5 hours

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Solve the equation
5m + 4m = 72

Answers

You add the 5m and 4m because they are like terms to get 9m=72 then divide both sides by nine to get m=8.

How to convert from point slope form to slope intercept form

Answers

Answer:

y=mx+(y_1-mx_1), b=y_1-mx_1

Step-by-step explanation:

The point slope form of the equation of a line is given as:

y-y_1=m(x-x_1)

The slope-intercept form of the equation of a line is given as:

y=mx+b

where: m=slope, b=y-intercept.

To convert from the point slope form to slope intercept form, follow these steps:

Step 1: Distribute the right hand side

y-y_1=m(x-x_1)\ny-y_1=mx-mx_1

Step 2: Isolate the y variable

y=mx-mx_1+y_1\ny=mx+(y_1-mx_1)

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The sum of three consecutive multiples of 4 is 444. Find these multiples.

Answers

Step-by-step explanation:

Let the first multiple of 4 be x and second multiple be (x + 4) and third multiple be (x + 8) ...[Since, the number are consecutive multiple of 4]

\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\n

:\implies  \sf x \:  + \:  x  \: +  \: 4 \:  +  \: x \:  +  \: 8  \: = \:  444 \n  \n  \n

:\implies \sf 3x \:  +  \: 12  \: =  \: 444 \n  \n  \n

:\implies \sf  3x  \:  = \:  444 \:  -   \: 12 \n  \n  \n

:\implies  \sf  3x \: =  \: 432 \n  \n  \n

:\implies  \sf x \:  =  \:  (432)/(3) \n  \n  \n

:\implies\underline{ \boxed{\sf x \:  =  \:  144}} \n

_________________

Therefore,

\bullet\:\:\textsf{First multiple of 4 = x = \textbf{144}} \n

\bullet\:\:\textsf{Second multiple of 4 = x + 4 = 144 + 4 = \textbf{148}} \n

\bullet\:\:\textsf{Third multiple of 4 = x + 8 = 144 + 8 = \textbf{152}}

First multiple of 4 is x = 144

Second multiple of 4 is x + 4 = 144 + 4 = 148

Third multiple of 4 is x + 8 = 144 + 8 = 152

What does it mean to be sad and lonely

Answers

Answer: It means depression

Step-by-step explanation:

Answer:

Being sad means your body has entered a mini-clinical state, bringing back grief and usually making you remember past traumas for no existential reason. Sadness can drive you to feeling alone - not isolated, but alone with your inner thoughts. Your interior feeling cold, and like no one is there to put their hand out and help you become warm again. Sadness can drive you to loneliness, and loneliness can lead you to depression. Depression inverts your brain waves and makes you feel useless, no-good, nothing useful, just a joke.  

Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Round to the nearest hundredth if necessary. The quotient of a number divided by 6 is 3.5.

Answers

Answer:

(n)/(6)=3.5

n= 21

Step-by-step explanation:

The equation is simple, you just have to reason the sentence, the quotient of a number, this means that the result of the division is 3.5, and the number has to be divided by 6, so the equation would end up looiking like this:

(n)/(6)=3.5

As 6 is dividing and you want to clear N, you just put it on the other side of the equation multiplying, and you end up with this:

n=6(3.5)

n=21

So your answer for this equation would be n= 6.

n/6 = 3.5
Multiply both sides by 6.
n = 21