This problem illustrates the limit derivation of a Poisson distribution from Binomial distributions. Suppose an average of 66 arrivals occur during a 30 minute interval. To count arrivals, divide the 30 minute interval into nn sub-intervals. On the previous problem, you found the probability pp of one arrival during a single sub-interval for each n given. Now, compute the (estimated) probability that there will be, in fact, exactly 6 arrivals during a 30 minute interval, with each probability model:
a. Using Binomial with n=30, the chance of 6 arrivals is estimated as:__________
b. Using Binomial with n=60, the chance of 6 arrivals is estimated as:__________
c. Using Binomial with n=100n=100, the chance of 6 arrivals is estimated as:________
d. Using Poisson, the chance of 6 arrivals is estimated as:________
Required:
Use a probability calculator, and enter answers in decimal form, rounded to at least four places after the decimal.
Answers
Answer:
1. 0.1795
2. 0.1693
3. 0.1657
4. 0.1606
Step-by-step explanation:
This problem was solved using the binomial distribution
1.
N = 30
P = 6/30 = 0.2
Using binomial distribution
30C6 x 0.2⁶ x 0.8²⁴
= 593775 x 0.000064 x 0.004722
= 0.1795
2.
N = 60
P = 6/60 = 0.1
60C6 x 0.1⁶ x 0.9⁵⁴
= 50063860 x 0.000001 x 0.00338139
= 0.1693
3.
N = 100
100C6 x 0.06⁶ x 0.94⁹⁴
= 1192052400 x 0.000000046656 x 0.00297864
= 0.1657
4.
Poisson distribution was used here
e^-6(6)⁶/6!
= 0.1606
Related Questions
PLEASE HELP!!!
There are 800 students who attend Park Middle School. There are 1.5 times as many boys as there are girls. Assign variables to the unknowns.
Answers
X is boys
And y are girls
I need help like serious help
Answers
Answer:
AB is equal to AD because if you move from A to B, you would have to go 3 points toward the B, and then move one point toward B. Same for D. You must move 3 points toward D, then move one down.
Step-by-step explanation:
find the value of x
I have to show the work
Answers
Answer:
x = 39
Step-by-step explanation:
A circle is made up of 360 degrees
235+ 54+ x+32 = 360
Combine like terms
x+321=360
Subtract 321 from each side
x+321-321 = 360-321
x = 39
209.106 in expender form
Answers
Answer:
209.106 = (2 x 100) + (0 x 10) + (9 x 1) + (1/10) + (0/100) + (6/1000)
Answer:
200+9+0.1+0.006.
Step-by-step explanation:
5 2/5 is ___ 3 1/2, is it greater than or less than
Answers
Answer:
5 2/5 > 3 1/2. 5 2/5 is greater than 3 1/2
Step-by-step explanation:
Answer:
I believe that 5 2/5 is greater than 3 1/2
Ivan has 32 baseballs and 48 basketballs. If he wants to divide them into identical groups without any balls left over, what is the greatest number of groups Ivan can make
Answers
Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.
Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:
48 = dividend
32 = divisor
Step 1:
Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:
3 2 ⟌ 4 8
Step 2:
The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
3 2 ⟌ 4 8
Step 3:
Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.
0
3 2 ⟌ 4 8
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
3 2 ⟌ 4 8
- 0
4
Step 5:
Move down the 2nd digit of the dividend (8) like this:
0
3 2 ⟌ 4 8
- 0
4 8
Step 6:
The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:
0 1
3 2 ⟌ 4 8
- 0
4 8
Step 7:
Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:
0 1
3 2 ⟌ 4 8
- 0
4 8
3 2
Step 8:
Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.
0 1
3 2 ⟌ 4 8
- 0
4 8
- 3 2
1 6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 48 divided by 32 calculated using Long Division is:
1
16 Remainder
2=10 3=18 4=28 6=54 then 8=?
Answers
Answer:
72
Step-by-step explanation:
2*5=10
3*6=18
6*8=54
8*9=72
Please answer question a & b.
a) Work out the following:
3/4 - 7/9 + 2
b). Which is the largest of the following numbers?
0.1, 0.02, 0.003, 0.0004, 0.00005
Please help due today.
Answers
Answer:
a)
b)0.1
pls refer to the pic
Which of the following numbers is a perfect square?
222
141
196
124
Answers
Answer:
196
Step-by-step explan
What’re these two problems simplified?
Answers
Step-by-step explanation:
-2(3x-12)+4-13
=-6x+24+4-13=-7x-15
=6x-15
4(5x-1)+8x-20=20x-4+8x-20
=28x-24
So this is ur solution.
But if u wnt to solve these eq. together thn it will be:-
6x-15=28x-24
6x-28x=-24+15
-22x=-9
x=22/9=2.44
Hope u like it.
Answer:
-8+9 is problem one
Step-by-st-ep explanation:
f(x) = -x^2+10x-6
Find f(-5)
Answers
9514 1404 393
Answer:
f(-5) = -81
Step-by-step explanation:
Put -5 where x is and do the arithmetic.
f(-5) = -(-5)^2 +10(-5) -6
f(-5) = -25 -50 -6
f(-5) = -81
Answer:
-81
Step-by-step explanation:
what is the solution of 7k+2=4k-10? (anwser asap plz)
1.- Divison property of Equality
2.- Simplify
3.-Subtraction Property of Equality
4.- Subtract
Answers
Answer:
3
Step-by-step explanation:
Answer:
k = -4
division property
Step-by-step explanation:
68% of johns school are boys. There are 180 more boys than girls. How many students are there in johns school
Answers
Answer:
500 students in the school
Step-by-step explanation:
100 - 68% = 32%
boys percentage 68%
girls percentage 32%
difference 68 - 32 = 36% = 180
36 ÷ 18 = 2 × 50 = 100
180 ÷ 18 = 10 × 50 = 500
Answer:
500 students.
Step-by-step explanation:
This a system of equations you could write where t is the total amount of students in the school, b is the number of boys, and g is the number of girls:
0.68t=b
b+g=t
180+g=b
0.68t+g=t
g=0.32t
180+g=b
180+0.32t=0.68t
180=0.36t
t=500
solve the linear equation 7x-3=67 for x
Answers
Answer: x=10
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
when we see something like 7x-3=67, we have to get x alone. the first step is to always cancel out the constant (the number that does not have a variable such as x connected to it). so to make -3 equal to 0 we have to add 3. what we do to one side we have to do to the other so after adding 3 on each side we get 7x=70. now here, we still have to get x alone. 7x means 7 times x so to undo this we have to do the opposite and divide each side by 7. 7 divided by 1 (and 1x is 1 times x which is just x so now we have x alone yaay) and 70 divided by 7 is 10. so x = 10.
I hope this helped :))
Solve for X please :(( Will give brainliest.
Answers
5x+6+92 = 22x-4
5x+98 = 22x-4
add 5x to both sides
98 = 27x-4
add 4 to both sides
102 = 27x
divide both sides by 27
x = 3 and [tex]\frac{7}{9}[/tex]
How to estimate the sum of using different methods. 187,176,154,207
Answers
Answer:
tuff
guess you will fail
Step-by-step explanation:
Determine the density in g/cm3 of a mineral that has a volume of 3.8 cm3 and a mass of 22.4 g.
Answers
Answer:
5.89 g/cm³
Step-by-step explanation:
givens,
Mass = 22.4 g
volume = 3.8 cm³
Density = mass / volume
= 22.4 / 3.8
= 5.89 g/cm³
The density with a volume of 3.8 cm³ and a mass of 22.4 g is 5.89 g / cm³.
Given,
The volume of a mineral = 3.8 cm3
And the mass of the mineral = 22.4 g
We need to find the density.
What is density?It is the ratio of mass and volume.
Density = mass / volume
Find the density.
Volume = 3.8 cm³
Mass = 22.4 g
Density
= Mass / Volume
= 22.4 / 3.8
= 5.89 g / cm³
Thus the density with a volume of 3.8 cm³ and a mass of 22.4 g is
5.89 g / cm³.
Learn more about how to find density in the cgs system here:
https://brainly.com/question/9989733
#SPJ6
The slope of a line is 15 and the point (3, -1) lies
on the line. Write an equation of the line in
point-slope form.
Answers
Answer:
The answer is
[tex] \huge y + 1 = 15(x - 3) \\ [/tex]
Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question we have the final answer as
[tex]y + 1 = 15(x - 3)[/tex]
Hope this helps you
A large cable company reports the following.
80% of its customers subscribe to its cable TV service.
41% of its customers subscribe to its Internet service.
31% of its customers subscribe to its telephone service.
25% of its customers subscribe to both its cable TV and Internet service.
20% of its customers subscribe to both its cable TV and phone service.
22% of its customers subscribe to both its Internet and phone service.
15% of its customers subscribe to all three services.
Consider the chance experiment that consists of selecting one of the cable company customers at random. Use the probability formulas of this section to find the following probabilities.
a. P(cable TV only)
b. P(Internet I cable TV)
c. P(exactly two services)
d. P(lnternet and cable TV only)
Answers
Answer:
Step-by-step explanation:
Let n(U) be total amount or customers = 100%
n(C) = 80% of its customers subscribe to its cable TV service.
n(I) = 41% of its customers subscribe to its Internet service.
n(T) = 31% of its customers subscribe to its telephone service.
n(CnI) = 25% of its customers subscribe to both its cable TV and Internet service.
n(CnT) = 20% of its customers subscribe to both its cable TV and phone service.
n(InT) = 22% of its customers subscribe to both its Internet and phone service.
n(CnInT) = 15% of its customers subscribe to all three services
number of those that subscribed to TV only = n(C) - (n(CnInT')+(n(CnI'nT)+(n(CnInT))
= 80-[(25-15)+(20-15)+15]
= 80-{10+5+15)
= 80-30
= 50
Hence 50% read cable TV only
Pr(cable TV only) = 50/100 = 1/2
2) number of people that read internet and cable TV = 25%
Pr(internet and cable) = 25/100 = 1/4
3) number of people that had exactly two services are;
n(cable and internet only)+n(internet and phone only)+(cable and phone only)
= (25-15)+(22-15)+(20-15)
= 10+7+4
= 21%
Hence 21℅ read exactly two services
pr(exactly 2 services) = 21/100
4) number of people that read internet and cable only = n(CnI) - n(CnInP)
= 25-15 = 10%
Pr(Internet and cable only) = 10/100 = 1/10
Scarlett stopped at a campground along the Appalachian trail. The campground had a 1
2
acre area for tents, divided into 6 equal campsites. Scarlett picked one of the sections to pitch her tent.
Which expression would give you the size of Scarlett’s campsite? Check all that apply.
One-half divided by 6
StartFraction 6 Over 7 EndFraction divided by 6
6 divided by one-half
StartFraction 6 Over 12 EndFraction divided by 6
6 divided by StartFraction 3 Over 6 EndFraction
Answers
Answer:
1/2 divided by 6
6/12 divided by 6
Step-by-step explanation:
Answer:
a - d
Step-by-step explanation:
a tourist information center charges $10 per hour to rent a bicycle
Answers
Answer:
10per the other side of alloys
PLEASE ANSWER, I WILL MARK BRAINLYEST. IF YOU PUT AN ABSURD ANSWER I WILL REPORT. 50+ POINTS
Answers
Answer:
The umbrella will fit in, but there will be a lot of extra room.
Step-by-step explanation:
Remember the Pythagorean theorem:
x^(2) + y^(2) = n^(2)
where "x" and "y" are the legs of the right triangle and "n" is the hypotenuse
In this problem it is given that the sides (legs) are:
38in, and 24in
and diagonally across is 29in
so the hypotenuse is 29in
therefore we can form the equation:
38^(2) + 24^(2) = 29^(2)
without solving it is clear that
38^(2) + 24^(2) > 29^(2)
because 38 is a leg, but it is greater than 29, which means that 38 - 24 - 29 is not a Pythagorean triple,
but because 38 > 29, then the 29 in umbrella will fit into the suitcase, but it will not be a snug fit, there will be a lot of extra room
Answer:
see below
Step-by-step explanation:
The umbrella should fit
The umbrella is the diagonal in a right triangle so we can use the Pythagorean theorem
a^2+b^2 = c^2
18^2 + 24^2 = c^2
324 + 576 = c^2
900 = c^2
Take the square root of each side
sqrt(900) = sqrt(c^2)
30 =c
As long as the umbrella is less than 30 inches, it should fit
The umbrella is 29 inches so it should fit
Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 20 elderly women gathered once a week to discuss different works of art. The study also included a control group of 20 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.
Required:
a. Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?
b. Explain why you think that the researchers included a control group in this study.
Answers
Step-by-step explanation:
1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.
2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.
An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn 5.6% interest, compounded monthly. Payments
will be made at the end of each month, Find the total value of the annuity in 16 years if each monthly payment is $65.
Do not round any intermediate computations, and round your final answer to the nearest cent
Answers
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
A Giant Sequoia tree is planted in Trevor's
backyard when it is 2 ft tall. The tree grows an
average of 4 ft each year. Write a function and
graph the height of the tree over this time period.
I need to know the answer and what points to graph please help
Answers
324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues
Answers
I will give brainliest :D
Which equation matches this scenario?
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61
Answers
Answer: 8x + 5= 61
Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.
Consider continuous functions f and g. Then complete the statement.
(See attachment)
The x-intercept of the function f is (greater than, equal to, or less than) the x-intercept of function g.
(Multiple choice in the parentheses)
Correct answer receives BRAINLIEST! Have a great day. ❤️
Answers
Using the concept of x-intercept, it is found that the correct statement is:
The x-intercept of the function f is greater than the x-intercept of function g.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = 0.In this problem, in function f(x), when f(x) = 0, x = 3, hence the x-intercept is x = 3.
Function g(x) is defined by:
[tex]g(x) = 2 + \sqrt[3]{3x + 1}[/tex]
Hence, the x-intercept of g(x) is found as follows:
[tex]g(x) = 0[/tex]
[tex]2 + \sqrt[3]{3x + 1} = 0[/tex]
[tex]\sqrt[3]{3x + 1} = -2[/tex]
[tex](\sqrt[3]{3x + 1})^3 = (-2)^3[/tex]
[tex]3x + 1 = -8[/tex]
[tex]3x = -9[/tex]
[tex]x = -\frac{9}{3}[/tex]
[tex]x = -3[/tex]
The x-intercept of g(x) is -3, which is less than the x-intercept of function f(x), hence, the correct statement is:
The x-intercept of the function f is greater than the x-intercept of function g.To learn more about the concept of x-intercept, you can take a look at https://brainly.com/question/24737967
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm.
What is its surface area?
Show your reasoning.
I got 48 cm2
Answers
Answer:
i got 48
Step-by-step explanation:
2(5*2)
2(2*5)
2(2*2)
rx:
x – 6 = -3x + 22
Answers
Answer:
X= 7
Step-by-step explanation:
4x = 28
X = 7