Answer:
Step-by-step explanation:
Using confidence interval concepts, it is found that:
a)
The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).
The interpretation is:
iii. We are 99% confident that this interval contains the true population mean.
b)
A sample size of 664 would be required.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm M[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The interpretation of a x% confidence interval between a and b is that we are x% confidence that the true population mean lies in this interval, thus, option iii is correct.
In this problem:
Survey of 2005 adults, thus [tex]n = 2005[/tex].27% believe in astrology, thus, [tex]p = 0.27[/tex].99% confidence interval, thus z has a p-value of [tex]\frac{1 + 0.99}{2} = 0.995[/tex], thus z = 2.575.Then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.575\sqrt{\frac{0.27(0.73)}{2005}}[/tex]
[tex]M = 0.026[/tex]
The interval is:
[tex]M - \pi = 0.27 - 0.026 = 0.244[/tex]
[tex]M + \pi = 0.27 + 0.026 = 0.296[/tex]
The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).
Item b:
Irrespective of the value of p, thus [tex]\pi = 0.5[/tex].Margin of error of [tex]M = 0.05[/tex], and we have to find n:[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 2.575(0.5)[/tex]
Dividing both sides by 0.05.
[tex]\sqrt{n} = 2.575(10)[/tex]
[tex](\sqrt{n})^2 = [2.575(10)]^2[/tex]
[tex]n = 663.1[/tex]
Rounding up:
A sample size of 664 would be required.
A similar problem is given at https://brainly.com/question/16807970
1. Find the slope of the line in the graph
A rectangular room is 1.6 times as long as it is wide, and its perimeter is 34 meters. Find the dimensions of the room.
Answer:
Step-by-step explanation:
x=1.6w and 2w+2x=34.
Simply substitute for x in the perimeter equation, and solve for w. Now compute x.
There are 130 people in a sport centre.
65 people use the gym.
51 people use the swimming pool.
44 people use the track.
15 people use the gym and the pool.
14 people use the pool and the track.
10 people use the gym and the track.
1 person uses all three facilities.
Given that a randomly selected person uses the gym and the track, what is the probability they
do not use the swimming pool?
Answer:
1/13
Step-by-step explanation:
there are 10 people that use the gym and track and 10 is 1/13 of 130
The first term of an arithmetic sequence is -5, and the tenth term is 13.
Find the common difference.
2
1.8
8/9
Answer:
Step-by-step explanation:
Let d be the common difference.
a₁₀ = a₁ + (10-1)d
13 = -5 + 9d
d = 2
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=69°, and FD = 64 feet. Find the length of DE to the nearest tenth of a foot.
Answer:
Step-by-step explanation:
A roller coaster is being designed that starts at (0,22) and ends at (19,2),
Along the ride there is a relative minimum at (5,6) and a relative
maximum at (10,18). The roller coaster is almost finished but one
section is missing. Find the correct function that completes the roller
coaster so that the ride is smooth and continuous.
Answer:
The function is, f(x) = 6·sin((π/5)(x + 3π/2)) + 12
Step-by-step explanation:
The general form of equation of a roller coaster is given as follows;
y = A·sin(B(x - C)) + D
Where;
A = The amplitude = (18 - 6)/2 = 6
D = The vertical shift = 12
One revolution = 10 unit
∴2·π = 10 unit
Therefore, 10 = 2·π/B
B = 2·π/10
The phase shift = 3·π/2
Therefore, we have the function as follows;
f(x) = 6·sin(2·π/10(x + 3π/2)) + 12 = 6·sin((π/5)(x + 3π/2)) + 12
Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school. He puts m mechanical pencils in each bag. He puts twice as many regular pencils in each bag. What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?M
Answer:
The total number of pencils that Mr. Moretti gives to his is 162.
Step-by-step explanation:
He puts 3 mechanincal pencils in each bag.
In each bag, there is also twice as many regular pencils, that is, 3*2 = 6 regular pencils.
So in each bag, 3 + 6 = 9 pencils.
What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?
18 students, and each gets 9 pencils.
18*9 = 162
The total number of pencils that Mr. Moretti gives to his is 162.
Answer:
162 pencils
Step-by-step explanation:
i did the i ready lesson!
find the mad: 250, 249, 251, 253, and 253
Its 250 for sure i have not done mads for a while now.
So maybe double check me with someone else
Answer:
It's 1.44
Step-by-step explanation:
Can someone help me with this question pls
Answer:1/6*1/6*1/6=1/216
Step-by-step explanation:
Please help me I will get you a thanks :-)
Answer:
A=32.5
Step-by-step explanation:
A=(4+9)*5/2
A=13*5/2
A=65/2
A=32.5
You are sending a package in the mail. The box is a cube
measuring 14 inches on all sides. How many cubic inches
is the package?
Answer: 2744
:)
Hope it’s right
The volume of a cube with a side length of 14 inches is 2744 cubic inches.
Side of the cube = 14 inches
What is the volume of a cube?The volume of a cube with side length a is a³.
So, the volume of a cube with a side length of 14=14³
The volume of a cube with a side length of 14=2744 cubic inches.
Hence, the volume of a cube with a side length of 14 inches is 2744 cubic inches.
To get more about cubes visit:
https://brainly.com/question/1972490
Find the area of the rectangle 2 1/4 1 1/2
Answer:
3 3/8
I converted the fractions in to decimals, multiplied them and then converted the decimal into a fraction.
Mr. Kramer bought his daughter a kitten for her birthday, so now he needs to buy cat food. First, he gets a 20-pound bag of dry cat food. Then, he finds a good deal on 3-ounce cans of wet cat food, so he buys 48 of them. How many pounds of cat food does Mr. Kramer get in all?
Answer: 29 lbs
Step-by-step explanation: If you do 48 times 3 you will get 144 and if you do 144 divided by 16 you will get 9 and if you do 9 plus 20 you will get 29 lbs in total.
The required pounds of cat food Mr. Kramer get in all is 9.
given that,
First, he gets a 20-pound bag of dry cat food.
Then, he finds a good deal on 3-ounce cans of wet cat food,
so he buys 48 of them.
It is to determine how many pounds of cat food Mr. Kramer get in all.
In mathematics, it deals with numbers of operations according to the statements.
In a can, there are 3 ounces of wet cat food.
1 can = 3 ounce
multiplying both sides by 48
48 can = 3 * 48 ounce
48 can = 144 ounce
1 pound = 16 ounce
1/16 pound = 1 ounce
multiplying both sides by 144 on both sides
144 / 16 pound = 144 ounce
9 pound = 144 ounce
Thus, the required pounds of cat food Mr. Kramer gets in all is 9.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
It’s worth 13 points thank you!
:)
Answer: the answer is the 3rd bubble:)
Step-by-step explanation:
Charles invested $15,000 in stocks and bonds. He made a 12% profit on his stock investments and a 5% profit on his bond investments. If Charles's combined profits on both types of investments were $1,450, how much did he invest in stocks?
Answer:When you leave the interest in your
account or reinvest the money you earn on your
investments, the money you earn starts to earn
money too. Over time, the magic of
compounding works, allowing your money to
grow with dramatic results. The more time you
have to save, the less money you need to save
because of compounding. And the longer you
wait to start saving, the more you have to spend
to reach your goal. For example, let’s assume
that Maria’s savings grow by 5% a year. If she
starts to save $243 a month now, it will cost her
$58,320 to have $100,000 in twenty years. If
she waits 10 years to start saving, she will have to
save $644 a month for 10 years, and it will cost
her $77,280 to reach $100,000 in twenty years.
Step-by-step explanation:Hope this helps!!!!
Answer:
$10,000 invested into stocks
Step-by-step explanation:
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known at 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes. Use a = 0.05. The test statistic is a 1.96 b. 1.64 c. 2.00 d. 0.056 The p-value is a. 0.0456 b. 0.0482 c. 0.4772 d. 0.9759 e. 0.9772 At the 5% level, you a. fail to reject the null hypothesis b. reject the null hypothesis
Answer:
The test statistic is c. 2.00
The p-value is a. 0.0456
At the 5% level, you b. reject the null hypothesis
Step-by-step explanation:
We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes.
This means that the mean and the alternate hypothesis are:
Null: [tex]H_{0} = 3[/tex]
Alternate: [tex]H_{a} = 3[/tex]
The test-statistic is given by:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Sample of 100 customers.
This means that [tex]n = 100[/tex]
3 tested at the null hypothesis
This means that [tex]\mu = 3[/tex]
The average length of time it took the customers in the sample to check out was 3.1 minutes.
This means that [tex]X = 3.1[/tex]
The population standard deviation is known at 0.5 minutes.
This means that [tex]\sigma = 0.5[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}[/tex]
[tex]z = 2[/tex]
The test statistic is z = 2.
The p-value is
Mean different than 3, so the pvalue is 2 multiplied by 1 subtracted by the pvalue of Z when z = 2.
z = 2 has a pvalue of 0.9772
2*(1 - 0.9772) = 2*0.0228 = 0.0456
At the 5% level
0.0456 < 0.05, which means that the null hypothesis is rejected.
A bouncy ball is dropped such that the height of its first bounce is 6.75
feet and each successive bounce is 68% of the previous bounce's
height. What would be the height of the 6th bounce of the ball? Round
to the nearest tenth (if necessary).
Step-by-step explanation:
0,4 ft
It can be convinient to let a spreedsheet compute the values for you
Here we have written an expiliclit formula for the height of the 9th bounce
H= 5.5 x 0.64'(n-1)
We have written the formuka this way beacause we are given the height of the firrrst bounce not the satrting height so as you see each bounce multiples the height by a factor of 0,64 then the 7th bounce will be
H= 5.5 x 0.64'6 = 0.378 = 0,4 feet
Hope it helpsAnswer: 1
Step-by-step explanation:
What is the solution to the following equation? X +(-13) = -5. A. X= 18 B. X = 8 C. x -18 D. X = -8
x + (-13) = -5
x - 13 = -5
x = -5 + 13
x = 8
The difference between x and 8 is equal to 15
Answer:
x = 23
Step-by-step explanation:
15 + 8 is 23 so x = 23
Testing:
H0:μ=54.5
H1:μ<54.5
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
Calculate the test statistic, rounded to 2 decimal places.
t=
Answer:
t = -1.54.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
H0:μ=54.5
This means that [tex]\mu = 54.5[/tex]
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
This means, respectively, that [tex]n = 48, \mu = 54.1, \sigma = 1.8[/tex]
Test statistic
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{54.1 - 54.5}{\frac{1.8}{\sqrt{48}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is t = -1.54.
A package delivery company experiences high variability in daily customer demand, which in turn results in high variability in the daily workload at the central sorting facility. The company relies on its sorting facility employees working overtime to provide on-time delivery when the workload demand is very high. A sorting facility employee receives a salary of $12/hour for a 40 hour week, and the employee receives $18/hour for every hour worked overtime, that is, for every hour worked over 40 hours in a given week. The number of overtime hours that an employee works in any given week is a random variable, with a mean of 15 hours and a standard deviation of 4 hours.
Required:
What are the mean, the standard deviation, and the variance of an employee's total weekly salary?
Solution :
Let :
X = number of overtime hours
S = total weekly salary
S = [tex]$12 \times 40 + 18 \times X$[/tex]
S = 480 + 18X
E(S) = [tex]$480 + 18 \times E(X)$[/tex]
[tex]$E(S) = 480 + 18 \times 15$[/tex]
= 750
Mean of S = 750
Var (S) = [tex]$18^2 \times Var(X)$[/tex]
Var(S) = [tex]$18^2 \times 4^2$[/tex]
= 5184
Variance of S = 5184
The standard deviation equals square root of 5184 = 72
A fair cube has 2 blue sides, 2 red sides, and 2 green sides.
What is the probability of rolling a blue or red side?
Nathan inherited $100,000 from a wealthy uncle and invested the money in an account that earns 4% interest compounded annually.
How much interest will this money earn if Nathan leaves it in the account for 10 years?
At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 68 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school?
Answer:
170
Step-by-step explanation:
2, 4, 6, 7, 6, 6, 6,3 What is the Mean? What is the Median? What is the Mode? What is the Range?
Answer:
Mean: 5
Median: 6
Mode: 6
Range: 5
hope that helps
Step-by-step explanation:
Mean = 5
Median = 6
Mode = 6
Range = largest no.- smallest no.
= 7-2 = 5
A family is trying to pick from different shades of paint for their living room. They have narrowed it down to 3 different blues and 6 different greens.
The family decides to just randomly select a color from these.
What is the probability they will pick a shade of blue?
Enter your answer to the nearest percent in the box.
For ratios, the numerator usually indicates how much of a specific option you have, and the denomenator is often times the total of the set.
In this case, you have a total of 9 shades, if you add the greens and blues together. Three of them, are blue.
Hopefully this helps!
Answer: yes
Step-by-step explanation:
i had this quesion too and i got it correct
find the ratio 3600sec is to 2hours
Answer:
30:1
Step-by-step explanation:
Which equation has a solution of 4? Select all that apply. A 12x = 3 C10 + x = 14 B 6x = 24 DX-4 = 8
Answer:
C and B
Step-by-step explanation:
A. 12x = 3, x =1/4
C. 10 + x = 14, x = 4
B. 6x = 24, x =4
D. x -4 = 8, x =12
Only the expression mentioned in B and C gives the solution as 4. Options B and C are correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
A
12x = 3
Simplifying the above expression,
12x = 3
x = 3 / 12
x = 1 / 4
Similarly simplifying all the expressions gives,
B. x = 4
C. x = 4
D. x = 12
Thus, only the expression mentioned in B and C gives the solution as 4. Options B and C are correct.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Given the system:
4x + 3y = -1
5x + 4y = 1
What is the solution to this system?
A. (-7,9)
B. (9,-7)
C. (-1,1)
D. (1,-1)
Answer:
A is the answer
Step-by-step explanation:
hope that helped
HELP ASAP
The radius of a quarter circle is 1.4 millimeters. What is the quarter circle's area?
Answer:
A = 1.5386
Step-by-step explanation:
Quarter circle area formula:
A = (πr²)/4
A= (π1.4²)/4
A = (3.14*1.96)/4
A = (6.1544)/4
A = 1.5386