Mathematics College

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.4 times every eight hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open.
(a) Explain why the Poisson probability distribution would be a good choice for the random variable r.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

What is ? (Round your answer to three decimal places.)


(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Round your answer to four decimal places.)


(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Round your answer to four decimal places.)


(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Round your answer to four decimal places.)

Answers

Answer 1

Using the Poisson distribution, it is found that:

a) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.b) 0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.c) 0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.d) 0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.

Item a:

In this problem, we are given the mean during an interval, which is a common event(1.4 every 8 hours), and intervals can be assumed to be independent, hence, the correct option is:

Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

Item b:

Mean of 1.4 every 8 hours, hence, every 11 hours, the mean is:

[tex]\mu = 11 \times \frac{1.4}{8} = 1.925[/tex]

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1459 = 0.8541[/tex]

0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.

Item c:

The probability is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

[tex]P(X = 1) = \frac{e^{-1.925}(1.925)^{1}}{(1)!} = 0.2808[/tex]

[tex]P(X = 2) = \frac{e^{-1.925}(1.925)^{2}}{(2)!} = 0.2703[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1459 + 0.2808 + 0.2703 = 0.697[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.697 = 0.303[/tex]

0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.

Item d:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]

0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.

To learn more about the Poisson distribution, you can take a look at https://brainly.com/question/13971530

Related Questions

MAX POINTS!!!! Please help me solve the problem in the picture and tell me what I’m doing also explain each step.

Answers

Answer 0.4
Regroup terms: 0.8 - j= -0.9j + 0.76
Add j to both sides: 0.8 = -0.9j + 0.76+j
Simply : 0.8=0.1×j+0.76
Subtract: 0.76 from both sides 0.8-0.76=0.1x j
Simplify 0.8−0.76 to 0.04: 0.04= 0.1×j
Divide both sides by 0.1: 0.04/0.1=j
Simply 0.04/0.1 to 0.4: 0.4 =j
Switch sides: j= 0.4

I know myself that the answer is 0.4

Simplify 1.25 (-x -4)

Answers

Answer:

-1.25x-5

Step-by-step explanation:

Multiply using Distribution:

1.25(-x-4)

-1.25x-5

My answer can't be simplified anymore, since there isn't any like terms.

A box contains four bags of sugar. The total mass of all four bags is 6 kg. What is the mass of each bag in grams?

Answers

The answer is 1500 grams

help me plssssssssssssss

Answers

Answer:

C .......

Step-by-step explanation:

Four tour buses depart the terminal on the same day. The itinerary of the first bus takes 6 days, for the second bus it takes 8 days, for the third bus it takes 10 days, and the fourth bus takes 15 days. Assuming that another tour begins the same day that the bus returns to the terminal, how many days will it take until all four buses return to the terminal on the same day?

Answers

Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.

Considering their itineraries, the number of days it will take until all four buses return to the terminal on the same day is the lcm of 6, 8, 10 and 15.

To find their least common factor, we factor each number by prime numbers, hence:

6 - 8 - 10 - 15|2

3 - 4 - 5 - 15|2

3 - 2 - 5 - 15|2

3 - 1 - 5 - 15|3

1 - 1 - 5 - 5|5

1 - 1 - 1 - 1

Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.

It will take 120 days until all four buses return to the terminal on the same day.

To learn more about the least common factor, you can take a look at https://brainly.com/question/24873870

At Cheesecake Factory, the cost of your meal before the tip is $77.23. You leave a 15% tip. How much
money did you leave for tip? What is the total cost of your meal?

Answers

Answer:

$88.81

Step-by-step explanation:

to find tip, multiply 77.23 and .15 to get $11.58

total cost = meal + tip

total cost = 77.23 + 11.58 which equals $88.81

34/23 as a decimal rounded to the nearest tenth

Answers

Answer:

1.5

Step-by-step explanation:

1.47826086

rounded to the nearest tenth is 1.5

QUESTION 17 PLEASE HELP ME ASAPP

Answers

Answer: change over time
Explanation: it is decreasing in height therefore is decreasing in altitude

Hey there!

• If it CHANGES it means your temperature/time changes a bit overtime

• If it CONSTANT your temperature/time remains the same

So, basically to this question it was INCREASED then it was DECREASED

Therefore, your answer is: “Option A. “

Because it didn’t stay same

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Tropical dried fruit costs $1.50 per pound and regular dried fruit costs $0.90 per pound. You want to create a mixed bag of tropical dried fruit and regular dried fruit that is worth $1.30 per pound. How many pounds of tropical dried fruit do you need if you have already purchased 50 pounds of regular dried fruit?

Answers

t = total amount of lbs of Tropical dried fruit

m = total amount of lbs of mixed bag

[tex]\begin{array}{lcccl} &\stackrel{fruit}{lbs}&\stackrel{per~lb}{price}&\stackrel{total}{price}\\ \cline{2-4}&\\ \textit{tropical fruit}&t&1.50&1.5t\\ \textit{regular fruit}&50&0.90&45\\ \cline{2-4}&\\ \textit{mix bag}&m&1.30&1.3m \end{array}~\hfill \begin{cases} t+50=m\\ 1.5t+45=1.3m \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 1st equation}}{1.5t+45=1.3\stackrel{m}{(t+50)}}\implies 1.5t+45=1.3t+65\implies 0.2t+45=65 \\\\\\ 0.2t=20\implies t=\cfrac{20}{0.2}\implies \boxed{t=100}[/tex]

Help help math math good luck

Answers

Angle 4 is 101°
Just find the last angle in the triangle and subtract that from 180.
The last angle in the triangle is going to be 180-52-49=79
Now subtract that from 180 since a straight line is 180°.
180-79=101
Also, your hint just says to add the two angles inside the triangle together. 52+49=101. So, there is two ways of doing it

Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation . ( Will Mark Brainliest if answered correctly).​

Answers

Step-by-step explanation:

I don't really know what demonstrating with rigid motion means, never heard that before. But a method for demonstrating it could be drawing circumferences of radius:

1) R1 = d(O,S)

2) R2 = d(O,J)

3) R3 = d(O,M)

With O being the origin of the reference system.

*Note: d(A,B) means distance between point A and point B

After you've done that you can show that the points S and P are on the same circumference, J and W are on the same circumference (different from the one of S and P), M and D are on the same circumference.

After you've done that you calculate the angle between the points on the same circumference and demonstrating that they are all the same.

Answer:

Step-by-step explanation:

Congruent

Shift right 1 unit and up 5 units

Rotate 90 degrees clockwise about (-1, 2)

Or

just rotate 90 degrees clockwise about (1, -1)

Solve for x: x /6−y/3= 1
SHOW WORK

Answers

[tex]\dfrac x6 - \dfrac y3 =1\\\\\\\implies \dfrac x6 - \dfrac{2y}6 = 1\\\\\\\implies \dfrac{x-2y}6 =1\\\\\\\implies x -2y =6\\\\\\\implies x =6+2y\\\\\\\implies x = 2(3 +y)[/tex]

HELP ANSWER PART A AND B

Answers

Answer:

part A: median is 12

part B: interquartile rage is 10

Step-by-step explanation:

Part A: to find your median on a box and whisker plot, you just need to look at your middle line in your box. In this case it's 12.

Part B: to find your interquartile range on a box and whisker plot, you subtract your Q1 and Q3. Your Q1 and Q3 will be the two outside lines that make up the rest of your box, in this case would be 6 and 16. To find your Q1 if you don't already have your plot set up, you separate the numbers that are given to you in half and find the median of each side. The first half will be your Q1 and the second half your Q3.

-5x + 7y = -3
-3x - y = 19

Answers

The answer is letter c

Answer:

x=-5, y=-4

Step-by-step explanation:

to solve this system of equations, first multiply the second equation by 7 to get -21x-7y=133. this allows for the y terms in both equations to cancel once you add the two equations together.

adding these together, the y term cancels and you are left with -26x=130. so dividing both sides by -26 will get x=-5. then plug this x value back into either original equation (i chose -3x-y=19) so solve for y.

-3(-5)-y=19 so -y=4 so y=4

so the answer to the system of equations is x=-5 and y=-4

What are the center and radius of the circle?

Answers

Answer:

R = 4

Step-by-step explanation:

Beause when we say (-1,4)

It say the center of it

need help solving this

Answers

Answer:

  x = (√21)/2

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. That means the middle-length side is (√3)/2 times the length of the longest side.

  x = (√3)/2·√7

  [tex]\boxed{x=\dfrac{\sqrt{21}}{2}}[/tex]

HELLO?? WHY ISNT ANYONE HELPING ME!!?!?!? HELP ME

Answers

Question 9 is 1 4/10 or 1 2/5. Question 8 is greater than. Question 7 is greater than. Question 5 is less than

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )

Answers

Answer:

x=7.85

Step-by-step explanation:

Give the triangles we know that:

[tex] \frac{cd}{fh} = \frac{de}{hg} = \frac{ce}{gf} [/tex]

Now we can substitute like usual

[tex] \frac{78}{fh} = \frac{117}{54} = \frac{ce}{5x + 1} [/tex]

Now we simplify the fraction in the middle

the middles fraction will =13/6

Therefore:

[tex] \frac{78}{fh} = \frac{13}{6} [/tex]

so 13fh=468

Therefore: fh=36

Now we can use the Pythagorean theorem

so

[tex]gf = \sqrt{ {54}^{2} - {36}^{2} } [/tex]

so gf=18√5

so 5x+1=18√5

so 5x=-1+18√5

so x=7.85

(I'm not too sure about this one tho)

Hello please help straight up answer I’ll give points thanks I’m just trying to pass

Answers

Answer:

I think it's 34°.

Step-by-step explanation:

The angle to the right of 3x+7 is the alternate interior angle to 2x+3, meaning that they are the same.

Now, that angle, 2x+3, and 3x+7, are on a line, which I'm assuming is a straight line with an angle of 180°. If it is, then (2x+3)+(3x+7)=180

Now you can solve for x.

2x+3+3x+7=180

5x+10=180

5x=170

x=34

Therefore, x=34°

Hope I helped!

Chang works as a tutor for $11 an hour and as a waiter for $13 an hour. This month, he worked a combined total of 90 hours at his two jobs. Let t be the number of hours Chang worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answers

Can you show more information please? I need more.

T = 90t + 90w

Step-by-step explanation:

90t = 90x11 = 990

90w = 90 x 13 = 1170

T = 90t + 90w

T = 990 + 1170

T = 2160




Help help help math math math

Answers

Answer:

1/4

Step-by-step explanation:

the x decreases by 1 the y decreases by 4

Answer:

-4

Step-by-step explanation:

Find all real values of $x$ such that $x^2-5x + 4=0$.

Answers

Answer:

x=4 && x=1

Step-by-step explanation:

x^2 - x - 4x + 4=0

x(x-1) - 4(x - 1)=0

(x-4)(x-1)=0

X=4 and x=1

All real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the quadratic equation is, x²-5x+4=0

Any equation of form ax²+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have to find the value of x as,

x²-5x + 4=0

x² - x - 4x + 4=0

x(x-1) - 4(x - 1)=0

(x-4)(x-1)=0

X=4 and x=1

Thus, all real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ6

Solve each system using substitution or additions
(elimination).

-x+2y=-1
5x-10y=6

Answers

Answer:

Step-by-step explanation:

L1 -x + 2y = -1

L2 5x - 10y = 6

-x + 2y = - 1 multiply by -1

x - 2y = 1 multiply by 5

5x - 10y = 5 is similar that 5x - 10y = 6

The system has no solution

Image attached giving 25 points please help

Answers

Irrational is the answer

A Math book is 6. 15 centimeters. How thick will 21 Math books on a shelf be? A. 130.15 cm B. 129.16 cm. C. 129. 15 cm. D. 128. 16 cm​

Answers

Multiply:

6.15 x 21 = 129.15

Answer: C. 129.15 cm.

There are 30 cats and 50 dogs at the local animal shelter. Of these animals, 15% were adopted last week. How many animals were adopted?

Answers

12 animals were adopted
ANSWER = 12 Animals adopted

Work:
30 + 50 = 80
80 x .15 = 12

I want a way to solve such a problem​

Answers

Answer: please calculate the answer.

Step-by-step explanation:\\ Bro use this formula (sum of all numbers of the question) \ no. of seen numbers.

Arithmetic mean = ( 24+124+243+...) \ 12

help me plssssssssssssssssssssss

Answers

Answer:

p < 319

Step-by-step explanation:

The simplified equation after clearing the decimals is
-12.2 + 2.8w - 8.8 = 1.05w

Answers

Answer:

-21=-4w

w=5.25

but you don’t want decimals

so- you round down

w=5

Step-by-step explanation:

You combine like terms, and then make sure your variable is alone, the only way to get it alone from a ”mixed number”  is to divide

you do the same thing to both sides

so divde each side by -4

-21/-4 = 5.25

or with it rounded down since it’s under a five

It’s 5 with the decimals removed

i hope this helps

Help!!! I will reward lots of points! QUESTION: At Walmart, 6 apples and 5 oranges cost $11. At Publix, 2 apples and 3 oranges cost $7. Set up a system of two equations which you will solve to find the cost of one apple and one orange. Also step by step

Answers

Answer: I do not think this problem is solvable; the cost of apples and oranges at the stores are different

Other Questions
does anyone know the title of this movie? The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Private colleges: 52.8, 43.2, 45.0, 33.3, 44.0, 30.6, 45.8, 37.8, 50.5, 42.0. Public colleges: 20.3, 22.0, 28.2, 15.6, 24.1, 28.5, 22.8, 25.8, 18.5, 25.6, 14.4, 21.8. Required:a. Based on your computation of the two sample means and the two sample standard deviations, find the degrees of freedom. b. What is the point estimate of the difference between the two population means?c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges. f(x) = 33xg(x) = 3x+2 anyone to help with this question Answer this for me please!! This is for the ones who knows and speak Spanish Write an equation in the formY = mx +b to represent the line on eachgraphy4032st14 - 2TIT1-23ha*HHSz Write a brief paragraph in French talking about what passetemps you like to do. Write at least seven sentences. _________ applies to objects that are 3-dimensional in nature and has height, width, and depth. Which sentence in this introduction paragraph is most clearly the thesis statement?(1) We all carry things with us as we go through life. These can be memories, skills, regrets, and so on. (2) The same is true of the characters in Tim O'Brien's short story about the Vietnam War, "The Things They Carried." (3) Much of the story is made up of lists of the equipment the soldiers carry, including how much each item weighs, (4) By focusing on the weight of the characters' equipment, O'Brien is able to communicate the weight of their feelings as well.A. Sentence 2B. Sentence 4C. Sentence 1D. Sentence 3Pls Help Me!! I am on the test!! Where does Peer pressure come into play in a relationship? In this discussion, you will discuss the cultural conflict in the United States during the 1920s.Begin your discussion by addressing the following prompt:During the 1920s, many Americans felt that their beliefs and values were being put to the test. Explain how the trial of Sacco and Vanzetti or the Scopes Trial reflected the cultural conflict in the United States. Provide evidence to support your response.Post a detailed response to the discussion prompt. Then do the following:Respond to a classmates post about how the trial of Sacco and Vanzetti reflected the cultural conflict in the United States.Respond to a classmates post about how the Scopes Trial reflected the cultural conflict in the United States. Describe why did you decided to go to college after graduating from high school or not to go to college after graduating from high school? help me please thank you A business employs many young workers who like to use their time off to travel to visit family or go on adventures. The human resource manager observes that when holidays do not fall on a Friday or Monday, workers are disappointed that having just one day off prevents them from traveling. Which would be the most effective way for the company to add to the value of the holiday schedule?A. by establishing policies for unpaid leaveB. by establishing policies for other situations that require time offC. by creating a more generous sick leave policyD. by using floating holidays to create long weekends of time off do aquatic animals living underwater can hear the sound produced outside the surface if water pls pls help i need help Help help math math math (1) On June 16, 1884, the first roller coaster in America opened at Coney Island, in Brooklyn, New York. (2) It was created by LaMarcus Thompson. (3) It traveled approximately six miles per hour and cost a nickel to ride. (4) By the turn of the century, there were hundreds of roller coasters around the Country.Pretend your job is to revise the preceding paragraph. Which sentence contains a capitalization error? Which of the following is NOT a function of the lens in the eye?It can perform minor adjustments for distance.It flattens when light rays from distant objects are to be focused.It is a light receptor that generates nerve signals that are sent to the brain.It maintains its spherical shape to view nearby objects. Learning Task 3: List down effects of having a healthy school environment inside each shape to complete the graphic organizer.