Part (a): Create a discrete probability distribution using the generated data from the following simulator: Anderson, D. Bag of M&M simulator. New Jersey Factory. Click on the simulator to scramble the colors of the M&Ms. Next, add the image of your generated results to the following MS Word document: Discrete Probability Distributions Discrete Probability Distributions - Alternative Formats . Use the table in this document to record the frequency of each color. Then, compute the relative frequency for each color and include the results in the table.

Part (b): Compute the mean and standard deviation (using StatCrunch or the formulas) for the discrete random variable given in the table from part (a). Include your results in the MS Word document.

Part (c): Add a screenshot of the entire completed MS Word document to the discussion board as part of your discussion response (do NOT upload the MS Word document).

Part (d): Comment on your findings in your initial response and respond to at least 2 of your classmate’s findings.

Answers

Answer 1

(a) Relative Frequency

Red 520.4

Orange 180.14

Yellow 160.12

Green 80.06

Blue 60.046

Brown 300.23

Total 1301

(b) We get the mean as 2.292 and SD as 1.69.

(c) The completed MS Word document screenshot is shown below:

(d) When the findings of the classmates are taken into consideration, it can be analyzed that the frequency of each color is different in each experiment, and thus, the probability distribution is different.

Part (a):

Discrete probability distribution using the generated data using the given simulator:

Anderson, D. Bag of M&M simulator.

New Jersey Factory.The table for the frequencies of each color of M&M is:

ColorFrequencies

Red52

Orange 18

Yellow 16

Green 8

Blue 6

Brown 30

Total 130

The relative frequencies are computed as follows:

ColorFrequencies

Relative Frequency

Red 520.4

Orange 180.14

Yellow 160.12

Green 80.06

Blue 60.046

Brown 300.23

Total 1301

Part (b):

Mean and standard deviation calculation for the given discrete random variable:

Mean = ∑x * P (x) = (5 * 0.4) + (4 * 0.14) + (3 * 0.12) + (2 * 0.06) + (1 * 0.046) + (0 * 0.23)

= 1.3 + 0.56 + 0.36 + 0.12 + 0.046 + 0

= 2.292

SD = √∑(x - μ)² * P(x)

= √((5 - 2.292)² * 0.4) + ((4 - 2.292)² * 0.14) + ((3 - 2.292)² * 0.12) + ((2 - 2.292)² * 0.06) + ((1 - 2.292)² * 0.046) + ((0 - 2.292)² * 0.23)

= √(3.5836 * 0.4) + (1.112376 * 0.14) + (0.111936 * 0.12) + (0.050496 * 0.06) + (0.718721 * 0.046) + (5.255264 * 0.23)

= √1.43344 + 0.15592704 + 0.01343232 + 0.00302976 + 0.03302566 + 1.20932272

= √2.8471772

= 1.68738051 ≈ 1.69

Part (d):

From the above computation, it is observed that the mean of the distribution is 2.292 and the standard deviation is 1.69.

Also, it is found that the color with the highest frequency is red (52), while the color with the least frequency is blue (6).

When the findings of the classmates are taken into consideration, it can be analyzed that the frequency of each color is different in each experiment, and thus, the probability distribution is different.

It can also be observed that the probability of the color green is relatively small compared to other colors.

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Related Questions

Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:
(a) lambda=.5
Pr=
(b) lambda=0.9
Pr=
(c) lambda=1.1
Pr=

Answers

The exponential distribution applies to the lifetimes of a certain component. Its failure rate is unknown. The probability that the component will survive the past 5 years assumes:

(a) lambda=.5

Pr= 0.082

(b) lambda=0.9

Pr= 0.082

(c) lambda=1.1

Pr= 0.036

In the exponential distribution, the failure rate is a degree of the way fast the factor is expected to fail. It is regularly denoted through the parameter lambda (λ).

The opportunity that a thing will continue to exist beyond a positive time may be calculated using the exponential survival function, which is given by:

[tex]Pr(X > t) = e^(-λt)[/tex]

where X represents the random variable denoting the life of the thing, t is the specific time, and e is the bottom of the herbal logarithm.

Now let's calculate the possibilities for each case:

(a) lambda = 0.5, t = 5

Pr(X > 5) = [tex]e^(-0.5 * 5)[/tex] ≈ 0.082

In this example, with a lambda of 0.5, the element has a notably low failure price. The opportunity of the thing surviving beyond 5 years is about 0.082, or 8.2%.

(b) lambda = 0.9, t =5

Pr(X > 5) = [tex]e^(-0.9 * 5)[/tex] ≈ 0.082

With a lambda of 0.9, the issue has a slightly higher failure rate as compared to the previous case. The probability of the aspect surviving beyond 5 years stays at about 0.082, or 8.2%.

(c) lambda = 1.1, t = 5

Pr(X > five) = [tex]e^(-1.1 * 5)[/tex]≈ 0.036

In this situation, with a lambda of one.1, the factor has a better failure fee. The possibility of the element surviving beyond 5 years decreases to approximately 0.036, or 3.6%.

In precis, the possibility of a component surviving the past five years in an exponential distribution relies upon the failure price parameter lambda.

A lower failure price ends in a higher chance of survival, at the same time as a higher failure price decreases the opportunity of survival. It is essential to don't forget these chances when assessing the reliability and toughness of additives in diverse packages.

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A rectangular hall is 55 feet long and 48 feet wide. How long is a walkway along the diagonal?​

Answers

Answer:

[tex]73[/tex]

Step-by-step explanation:

[tex]73=\sqrt{55^{2} +48^{2} }[/tex]

Can someone pleaseeee helppp i dont know how to do this

Answers

Answer:

C=3e

Step-by-step explanation:

Slope=

At the 90% Confidence Interval, what are the (lower bound; upper bound)?

Answers

The lower bound of the interval is given as follows:

28.1.

The upper bound of the interval is given as follows:

29.9.

What is a t-distribution confidence interval?

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 30 - 1 = 29 df, is t = 1.6991.

The lower bound of the interval is given as follows:

[tex]39 - 1.6991 \times \frac{3}{\sqrt{30}} = 38.1[/tex]

The upper bound is given as follows:

[tex]39 + 1.6991 \times \frac{3}{\sqrt{30}} = 39.9[/tex]

Missing Information

The complete problem is:

"If n=30, (x-bar)=39, and s=3, at the 90% Confidence Interval, what are the (lower bound; upper bound)".

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Over which interval does f(t) have positive average rate of change?

A) -8,-2
B) -5,-1
C) -9,-8
D) 2,4

Answers

Answer:

D) 2,4

Step-by-step explanation:

The only answer with positive numbers

Answer:

D) 2,4

Step-by-step explanation:

How to divide 49 yd in the ratio 1:6?​

Answers

Answer:

7:42

Step-by-step explanation:

First off you add the ratio together-

6+1=7

Then you divide-

49÷7= 7

7 is equal to 1 in this ratio.

To write out the ratio you need to multiplicate-

7×1=7

and

6×7= 42

Leaving the as-

7:42

Answer:

7:42  

Step-by-step explanation:

First, add up the two numbers in the ratio to get 49.

Next, divide the total amount by 49, i.e. divide £16 by 8 to get £5. £5 is the amount of each 'unit' in the ratio.

Then you need to divide the total amount using that number i.e. 49/16 = 7/42.

To work out how much each person gets, you then multiply their share by the ratios. Therefore, the answer is 7 yd and 42 yds.

Solve the system using substitution: x = -4y and x + 5y = 2
Please and thank you.

Answers

Answer:

x = - 8, y = 2

Step-by-step explanation:

[tex]x = - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x = - 4y \: in \: equation \: (2) \\ - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x = - 4(2) \\ x = - 8\\[/tex]

(50 POINTS) Write out each sum.

Answers

Step-by-step explanation:

12. n^2+2n

if you insert 1 for k and then work up by inserting 2 for k and adding those together and stoping at n.

13. 8-2(2^n)

if you insert 3 for k and then work up by inserting 4 for k and adding those together and keep on going but stopping at n.

Hope that helps :)

Eu tenho um ovo de páscoa que custa 24,99 e tem 185 gramas, tbm tenho uma barra de chocolate q custa 5,10 e tem 90 gramad. Qual da mais vantagem para mim?

Answers

Answer:

A maior vantagem para mim é a barra de chocolate.

Step-by-step explanation:

Temos que encontrar o custo de 1 grama de ovo de Páscoa e barra de chocolate

Para o ovo de páscoa

Tenho um ovo de Páscoa que custa 24,99 e tem 185 gramas.

185 gramas = 24,99

1 grama = x

Multiplicação cruzada

185 gramas × x = 1 grama × 24,99

x = 1 grama × 24,99 / 185 gramas

x = 0,1612258065

Aproximadamente = 0,16

O custo de 1 grama de ovo de Páscoa = 0,15

Para a barra de chocolate

Também tenho uma barra de chocolate que custa 5,10 e tem 90 gramas.

90 gramas = 5,10

1 grama = x

Multiplicação cruzada

90 gramas × x = 1 grama × 5,10

x = 1 grama × 5,10 / 90 gramas

x = 0,0566666667

Aproximadamente = 0,06

O custo de 1 grama de barra de chocolate = 0,06

A maior vantagem para mim é a barra de chocolate.

tricia runs 520 meters each day for 3 days. how many total kilometers does tricia run in these 3 days?

Answers

Answer: 1.56 kilometers

Step-by-step explanation:

you multiply 520 by 3 because she ran for three days

so she ran 1560 meters

1000 meters= 1 kilometer

that makes it 1.56 kilometers

pls helpppppp !!
tysmmmm <33

Answers

Answer:

180

Step-by-step explanation:

From basic rules of a triangle we know that the interior angles of a triangle have to add up to equal 180°

But here is a formula for future references for finding the sum of the interior angles

interior angle sum = (n-2)180

where n = number of sides

and here is an example:

a triangle has 3 sides so we plug in 3 for n

(3-2)180

3-2=1

1*180 = 180

so the interior angles add up to equal 180

Students plant 148 flowers at a community park. Seventy-eight percent of the flowers are pansies. Use
rounding to estimate how many flowers are pansies

Answers

About 115 are pansies when you round down from the original number (115.44)

Find the volume of a cylinder with a diameter 4 mm and a height 8 mm.

Answers

Answer:100.53mm

Step-by-step explanation:

4th grade math helplolll

Answers

Answer:

175 dollars

Step-by-step explanation:

from that word problem the equation that i was able to get out of it was

1225/ 7

^ the travel allowance and how much days they are going to be there

i dont know if you are allowed to use a calculator in your class but puting 1225/ 7 does give you a answer of a positive number of 175 dollars

meaning that they can only use 175 dollars a day so they dont go over the allowance

i hope this helps you! please stay safe and have a good day :)

Answer:

Um, the answer for that is 175.

Step-by-step explanation:

all you need to do is divide $1,225 by 7 which is 175.

For each of the following questions, draw the phase portrait as function of the control parameter μ. classify the bifurcations that occur as μ varies, and find all the bifurcation values of μ .
1. θ = μ sin θ - sin 2θ
2. θ = sin θ/ μ+cos θ
3. θ = sin θ / μ + sin θ
4. θ = μ + cos θ + cos 2 θ
5. θ = μ sin θ + cos 2θ
6. θ = sin 2θ/ 1 + μ sin θ

Answers

Phase portrait as a function of the control parameter μ and the classification of bifurcations that occur as μ varies in the following questions are:

1. θ = μ sin θ - sin 2θA) μ<0, stable equilibrium at θ = nπ, where n is an odd integerB) μ>0, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero even integer. Hence, we have homoclinic bifurcation at μ = 0.

2. θ = sin θ/ μ+cos θA) μ<1, stable equilibrium at θ = nπ, where n is an integerB) μ>1, stable equilibrium at θ = sin−1 (μ) + nπ, where n is an integer. Hence, we have a pitchfork bifurcation at μ = 1.

3. θ = sin θ / μ + sin θA) μ<−1, stable equilibrium at θ = nπ, where n is an integerB) μ>−1, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero integer. Hence, we have homoclinic bifurcation at μ = −1.

4. θ = μ + cos θ + cos 2θA) μ>−1, stable equilibrium at θ = nπ, where n is an even integerB) μ<−1, no equilibrium point exists. Hence, we have fold bifurcation at μ = −1.

5. θ = μ sin θ + cos 2θA) μ>0, stable equilibrium at θ = sin−1 (−μ) + 2nπ, where n is an integerB) μ<0, stable equilibrium at θ = sin−1 (−μ) + (2n+1)π, where n is an integer. Hence, we have pitchfork bifurcation at μ = 0.

6. θ = sin 2θ/ 1 + μ sin θA) μ<−1, unstable equilibrium at θ = nπ/2, where n is an odd integerB) μ>−1, unstable equilibrium at θ = 0, stable equilibrium at θ = π. Hence, we have pitchfork bifurcation at μ = −1.

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You surveyed the number of tree species along the American River watershed, and obtain the following data set. Please respond to the following questions. Species a b Forest A Number 10 8 3 Forest B Number 5 6 0 7 10 Forest C Number 8 8 5 2 NINO d 1 e 1 2 Which forest has the lowest species richness, A, B, or c?

Answers

After considering the given data and analysing the information carefully we conclude that the lowest species richness observed is Forest A with only 18 species.

Let us get into the explanation part by first keeping in mind that to determine this, we need to evaluate the total number of species in each forest.

From the given data set, we clearly see that Forest A has 18 species, Forest B has 28 species, and Forest C has 25 species.

Hence, Forest A has the lowest species richness with only 18 species then Forest A has the lowest species richness among the three forests.

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help me bros, this question is a big part of my grade!!

Answers

Answer:

6.

m1 : 61

m2 : 61

m3 : 29

7.

m1 : 87

m2 : 45

m3 : 45

m4 : 52

Help ASAP! Find The Area Of A Circle With R =20.5

Answers

Answer:

Step-by-step explanation:

Pi*r^2 = Area

20.5^2 * Pi = 1320.25

Find the volume of this triangular pyramid.

Answers

Answer:

v = 340 cm³

Step-by-step explanation:

base area = 12 x 10 x 0.5 = 60 cm²

v = 60 x 17 x 1/3 = 340 cm³

50 POINTS! Name a pair of whole numbers that have a geometric mean of 4.

How many pairs of rational numbers have a geometric mean of 4?

please help and don't say something random just for the points :)​

Answers

Answer:

0, 16

1, 15

2, 14

3, 13

4, 12

5, 11

6, 10

7, 9

8, 8

Step-by-step explanation:

Any two numbers that have the product of positive 16 have a geometric mean of 4.

A spinner has five equal sections labeled 1-5. In 60 spins, how often can you expect to spin a 3?

Answers

ok so lets say that you have a pizza cutted out in 5 sections and want to pick up only a certain piece, let's say pepperoni. If you took a piece at random, the chances of getting that certain piece of pepperoni in 60 spins is:    12 / 60

Consider the following scenario. Suppose that
1000 people are involved in a conspiracy.
Suppose that every single individual involved in
the conspiracy can be trusted 99.9%, that is,
there is a 0.01% probability they reveal the
secrets of the conspiracy to the media within 50
years. This probability is the same for everyone
involved, and never changes over the course of
the 50 years. Moreover, suppose that the event
where anyone goes to the media (or not) is
independent if anyone else has (or hasn't)
already.
What is the probability that at least one
person involved in the conspiracy reveals their
involvement to the media within 50 years?

Answers

The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.

Consider the following scenario: There are 1000 individuals involved in a conspiracy.

Every person involved in the conspiracy can be trusted 99.9%, which means that there is a 0.01% probability that they will reveal the secrets of the conspiracy to the media within 50 years.

The probability of revealing the conspiracy is the same for everyone involved and remains constant throughout the 50 years.

Additionally, the probability of someone revealing the conspiracy is independent of whether anyone else has already done so or not.

What is the likelihood that at least one person will reveal their involvement to the media within 50 years? We can use the binomial distribution to determine the probability that at least one person in the conspiracy will reveal their involvement in the media in 50 years.

We'll use the following formula for the binomial distribution: P(X ≥ 1) = 1 - P(X = 0) where X is the number of individuals that reveal the secrets of the conspiracy.

In this situation, we know that there are 1000 people in the conspiracy, and the probability that each person will reveal the conspiracy is 0.01%.

We can therefore use the formula for the binomial distribution to solve for the probability of at least one person revealing the conspiracy:

P(X ≥ 1) = 1 - P(X = 0) P(X ≥ 1) = 1 - [tex](0.999)^{1000}[/tex] P(X ≥ 1) ≈ 0.994

Therefore, The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.

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Solve the word problem using the plotted points on the graph.

Answers

Answer:

In the graph, we can see that the relation between length and weight is given by the adjusted line, which passes through the points (24, 16) and (28, 25)

Remember that a linear relation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be calculated as:

a = (y₂ - y₁)/(x₂ - x₁)

Then in our case, the slope will be:

a = (25 - 16)/(28 - 24) = 9/4

y = (9/4)*x + b

Knowing that this line passes through (24, 16), we know that when x = 24, y must be equal to 16.

If we replace these in the equation, we can find the value of b.

16 = (9/4)*24 + b

16 = 54 + b

16 - 54 = b - 38

Then the equation is:

y = (9/4)*x - 38

Now that we know the equation, we can simply replace y by 34 pounds to find the value of x.

34 = (9/4)*x - 38

34 + 38 = (9/4)*x

72*(4/9) = x = 32

So we can estimate that the length of a fish that weighs 34 pounds is 32 (I do not know the unit of length, I can't see the horizontal axis on the image)

If $120.99 is charged for 654 units of electricity used,find the cost of one unit of electricity

Answers

divide 654 by 120.99
which equals $5.41

Answer:

$5.41

Step-by-step explanation:

654 divided by 120.99=5.405... therefore the answer is $5.41

Gary is 4 years less than three times his brothers age, \displaystyle bb. The sum of Gary and his brothers' age is 52. Write an equation to represent this relaitonship.
(PLS HELP ME WITH THAT QUESTION! IF YOU HELP ME I GIVE YOU BRAINLIEST I SWEAR)

Answers

Let x be the age of Gary’s brother.
x + (3x - 4) = 52

can someone pls simplify this
[tex] \frac{105}{12} [/tex]

Answers

25/3..................

What is the simple interest on $4,000 for 2 and a half years at 4 percent a year?

Answers

Answer:

Step-by-step explanation:

You can't receive money if you withdraw in the midst of a year.

So 4000 * 1/25 * 2 = $4320

A new experimental tank is in the shape of a cone, cylinder and sphere. All of the tanks have a volume of 10,000 cm3 . One condition to this tank is that the Radius should be 10 cm. Follow up the questions below based on this scenario.
Find the height of cylinder . Keep the answer in terms of π

Answers

Answer:

100/π cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Volume = 10,000cm³

Radius = 10cm

The formula for the height of a cylinder is obtained as:

V = πr²h

h = V/ πr²

h = 10000 /π × 10²

h = 10000 /π × 100

h = 100/π cm

The height of the cylinder in terms of π = 100/π cm

Find a solution, an, for the recurrence relation given below where ao = 7, a1 = 8 and for n > 2 an = -20 x an-1-90 x an 2

Answers

The solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1.

Given the recurrence relation,ao = 7, a1 = 8 and for n > 2 an = -20 x an-1-90 x an 2.

To find the solution, an, of the recurrence relation we need to follow the below steps.

Step 1:Find the general formula for the recurrence relation. We have an = -20 x an-1-90 x an 2. This is a second-order recurrence relation.

To solve a recurrence relation of this order, we assume the solution of the form an = r^n.Then substituting this value of an in the given relation we have r^n = -20r^(n-1) - 90r^(n-2).

Dividing both sides by r^(n-2), we have the characteristic equation r^2 = -20r - 90.On simplifying the above equation we get, r = 10 and r = -9.

Now, the general solution for an is given by, an = c1 * (10)^n + c2 * (-9)^n.

Step 2:Find the value of constants c1 and c2. We have a0 = 7 and a1 = 8.

Substituting n = 0 in the above general formula for an, we get c1 + c2 = 7.

 Substituting n = 1 in the above general formula for an, we get 10c1 - 9c2 = 8.

On solving the above two equations we get, c1 = (25)/19 and c2 = (102)/19.

Hence, the solution to the given recurrence relation is,an = (25/19)*(10)^n + (102/19)*(-9)^n.

The solution is valid for n > 1.

Therefore, the solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1. This is the required answer.

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The star running back on our football team got most of his total yardage running. The rest was catching passes. He caught passes for 60 yards. His total yardage was 150 yards. The running back for the other team got 200 yards. How many yards did the star running back on our football team get running?

Answers

Answer: The other team is extra information. 150 – 60 = 90

He got 90 yards running.

Step-by-step explanation:

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