In the division problem 8 ÷ 2 = 4, which is the dividend?

Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 p

djverab [1.8K]

Answer:

The probability that a given user is transmitting is 0.1 = 10%.

The probability that at any given time, exactly n users are transmitting simultaneously is $P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}$ .

0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.

Step-by-step explanation:

Binomial probability 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Each user transmits only 10 percent of the time.

This means that $p = 0.1$

Find the probability that a given user is transmitting.

The probability that a given user is transmitting is 0.1 = 10%.

Suppose there are 120 users.

This means that $n = 120$

Find the probability that at any given time, exactly n users are transmitting simultaneously.

This is $P(X = n)$ .

This n is different from the n of total number of users(120 in this case) from the standard binomial formula. This is the number of successes, which is the equivalent of x. So

$P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}$

The probability that at any given time, exactly n users are transmitting simultaneously is $P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}$

Find the probability that there are 21 or more users transmitting simultaneously.

Now we use the binomial approximation to the normal. We have that:

$\mu = E(X) = np = 120*0.1 = 12$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.1*0.9} = 3.2863$

Using continuity correction, this probability is $P(X \geq 21 - 0.5) = P(X \geq 20.5)$ , which is 1 subtracted by the pvalue of Z when X = 20.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20.5 - 12}{3.2863}$

$Z = 2.59$

$Z = 2.59$ has a pvalue of 0.9952

1 - 0.9952 = 0.0048

0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.

7 0

3 years ago

Abigail's mom asked her to go to the store and purchase 5 kilograms (kg) of potatoes. When she got to the store, she saw the pot

Over [174]

1 kilogram = 2.205 pounds

5 kg * 2.205 lbs = 11.0231 pounds

Round to pounds = 11
Round to tenths/1 decimal = 11
Round to hundredths/2 decimals = 11.02

5 0

3 years ago

Identify the pattern.Write the next 3 terms in each sequence. 83,75,67,59...

ExtremeBDS [4]

The pattern is the subtract 8 from the previous number.

So the next number: 59 - 8 = 51

And the next: 51 - 8 = 43

And the next: 43 - 8 = 35

4 0

4 years ago

Read 2 more answers

Which of the following are equivalent ratios?<br>A: 12 : 16<br>B: 3 : 5<br>C: 2 : 3<br>D: 6 : 8

Alla [95]

The equivalent ratios are A and D.

Here's an explanation:

When you look at D, you see that 12 is a multiple of 6, and 16 is a multiple of 8. So you know that it looks like they're equivalent. Then you test it out, 12/2=6. 16/2=8. so 12:16 = 6:8. Eyeballing it first can save time sometimes.

8 0

4 years ago

(10 points) Ben, Max, and Yolanda are at the front of three separate lines in the cafeteria waiting to be served. The serving ti

Alex777 [14]

Answer:

1/2 ; 1/3 ; 1/6

Step-by-step explanation:

Given :

Ben ~ exp(1)

Max ~ exp (2)

Yolanda ~ exp(3)

Ben :

X ~ exp(1)

Max:

Y ~ exp(2)

Yolanda :

Z ~ exp(3)

Probability that Yolanda is served first :

P(Z < (X, Y)) = Z /(x + y + z) = 3 /(1 + 2 + 3) = 3/6 = 1/2

Probability that Ben is served before Yolanda :

P(X < Z) = 1/ (1 + 2) = 1/3

Expected waiting time for first person served :

First person served = 1

Total = (1 + 2 + 3) = 6

Expected waiting time; E(x) :

E(x) : 1 / 6

4 0

3 years ago