Answer:
(1) 0.058
(2) 601
Step-by-step explanation:
(1)
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p\\[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 350 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of adults in a certain country work from home.
Compute the probability that fewer than 42 out of a random sample of 350 adults will work from home:
Sample proportion: [tex]\hat p=\frac{42}{350}=0.12[/tex]
[tex]P(\hat p < 0.12)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.12-0.15}{\sqrt{\frac{0.15(1-0.15)}{350}}})\\\\=P(Z<-1.57)\\\\=0.05821\\\\\approx 0.058[/tex]
Thus, the probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.058.
(2)
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
MOE = 0.04
Confidence level = 95%
Assume that the sample proportion is 50%.
The critical z-value for 95% confidence level is 1.96.
Compute the required sample size as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.50(1-0.50)}}{0.04}]^{2}\\\\=600.25\\\\\approx 601[/tex]
Thus, the required sample size is 601.
1. Using the normal approximation to the binomial, it is found that there is a 0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
2. Solving the equation for the margin of error of a confidence interval of proportions, it is found that we must survey 601 randomly selected teenagers.
Question 1:
Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
15% work from home, thus [tex]p = 0.15[/tex].Sample of 350 adults, thus [tex]n = 350[/tex]Then, for the approximation:
[tex]\mu = np = 350(0.15) = 52.5[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{350(0.15)(0.85)} = 6.68[/tex]
Using continuity correction, the probability is [tex]P(X < 42 - 0.5) = P(X < 41.5)[/tex], which is the p-value of Z when X = 41.5. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41.5 - 52.5}{6.68}[/tex]
[tex]Z = -1.65[/tex]
[tex]Z = -1.65[/tex] has a p-value of 0.05.
0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
Question 2:
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 z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Within 4%, thus [tex]M = 0.04[/tex].We do not have an estimate for the true proportion, thus [tex]\pi = 0.5[/tex].95% confidence level, thus z has a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], thus z = 1.96.We have to solve for n, then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96(0.5)}{0.04})^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
We must survey 601 randomly selected teenagers.
A similar problem is given at https://brainly.com/question/24261244
Is [tex]\sqrt{103}[/tex] irrational or rational? What is your reasoning?
Answer: irrational
Step-by-step explanation:
[tex]\sqrt{103}[/tex] is an irrational number because it is not a perfect square. Irrational numbers keep on terminating, so the answer to the question is irrational.
Hope this helps you!
Use a double integral in polar coordinates to find the area of the region. The region inside the circle (x − 4)2 + y2 = 16 and outside the circle x2 + y2 = 16
Answer:
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
Step-by-step explanation:
From the information given:
Lets first change the given relations into polar coordinates
So, the region of the inner circle into polar coordinates is as follows:
(x - 4)² + y² = 16
x² + y² - 8x = 0
r² - 8r cos θ = 0
r = 8 cos θ
For the outside circle:
x² + y² = 16
r² = 16
Thus, the intersection point are:
64cos²θ = 16
cos²θ = 1/4
θ = -(π/3) , (π/3)
Now: if we are to represent the sketch on a graph, the region of the integration D will be:
[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]
Therefore, the are of the required region can now be computed as follows:
[tex]A = \int \int _D \ dA[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]
[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]
[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]
[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
The double integral formula for the area of a given curve is described below:
[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)
Where:
[tex]r[/tex] - Distance with respect to origin.[tex]\theta[/tex] - Angle in standard position.We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:
[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]
Now we proceed to integrate the expression:
[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
We kindly invite to check this question on double integrals: https://brainly.com/question/2289273
The following are score of student in a test
As 75 75 70 70 65 65
65 ss ss 55 55 55 S S
40 35 35
35 35.The mean absolute deviation
Express x^2+y^2+4x-6y+1=0 in polar coordinates form
Answer:
Step-by-step explanation:
d over d x over y=-1 over 2 y plus 3 over 2
I need this in standard form slope intercept and point slope form.
Answer:
m= 3/4
Step-by-step explanation:
Use the slope formula to find the slope m
uiz
Select the slope-intercept form of an equation for a line with y-intercept -5 and slope 2.
A. x = 2x + 5
B. y = 2x - 5
O C y = 5x – 2
a
D. y = -5x + 2
Answer the question in the picture.
Answer: J = 33
Step-by-step explanation:
the corner of the triangle is 90 degrees so
90 + 57 = 147
Now the rest is 33 degrees.
Since it'll equal to 180 degrees.
Answer:
It's 33 degree
explanation:
Two triangles are similar so
angle K is equal angleQ=90DEGREE
ANGLE J=AngleP=33
En un molino azucarero cada trabajador recibe un bono mensual de $100.00 el trabajadorbtiene la opcion de gtar dicho bono comorando azucar de ingenio a un precio preferencial de 9.75 el kilogramo
suponiendo que dispone de $100 pesos extras para comprar
¿a partir de cuantoa kilogramos el trabajos empieza a pener de su dienero?
¿cual es la expresion algebraica que representa la situacion del trabajador?
HELPPPPPPP PLEASEEEEE
Answer:
b = 9
Step-by-step explanation:
Hello, once again.
Perpendicular lines have negative reciprocal slopes.
The slope would be -2.
Plug the y and x values in.
y = -2x + b
5 = -2(-2) + b
5 = -4 + b
b = 9
An annual pass to a park costs $120. Use a percent model to find 200% of the full price of the annual pass.
200% of the full price is $_________
Answer:
wouldn't be $240 why u keep deleting my answer
Answer:
?
Step-by-step explanation:
awetfhgyjuhk
Who ever gets it right gets brainliest
Answer:
sea mount I think
I have no clue but that's my guess
Anyone know this or could help me out?
On Saturday, Hattie biked 37.5 miles. On Sunday, she biked 35.75 miles. How far did she bike on Saturday and Sunday?
Answer:
Hattie travelled 73.25 miles on Saturday and Sunday
What is the measure of
m
∠
A
?
Answer:
I think it would be 22
Step-by-step explanation:
A bus took a six hour trip and traveled 225 miles. The speed was 40 mph for the first part of the trip, and then decreased to 25 mph for the second part of the trip. How many hours were traveled at each speed?
Answer:
The bus traveled at 40 mph for 5 hours, and at 25 mph for the last hour.
Step-by-step explanation:
The time for the first part is t. Therefore the time for the second part if (6-t).
40t + 25 (6-t) = 225
40t + 150- 25t = 225
15t = 75
t=5
Which values from the set make this inequality true?
4n<16 ; {1, 2, 3, 4}
Select each correct answer.
1
2
3
4
Answer:
1 2 3
Step-by-step explanation:
4 * 1 <16 4 is less than 16
4 * 2 <16 8 is less than 16
4 *3 <16 12 is less than 16
4 * 4 is not less than 16. 16 is not less than 16
What is the value of x?
A.3
B.4
C.6
D.8
Need help ASAP no rock
5) Solve for x:6) Solve for x:
X - 7.5 = 18.45x = 14.5
You made a typo here. There are TWO equal signs. Post the correct question.
AC=39 Find the length of AB
Answer:
AB = 12
Step-by-step explanation:
PLS answer fast!!!! I am literally in tears. Brainliest to the first person to answer it correctly
Answer:
-682
Step-by-step explanation:
I worked it out and got -682
The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1,4) and
B(4,1). Find the equation of the line that contains the given segment.
The line segment is AB.
The equation is y =
Answer:
y = - x + 5
Step-by-step explanation:
A(1, 4)
B(4, 1)
[tex]m_{AB}[/tex] = [tex]\frac{1-4}{4-1}[/tex] = - 1
y - 1 = - 1 ( x - 4 )
y = - x + 5
Frank’s Pizzeria has a champion pizza eater named Sandy who can eat 61⁄2 slices in 2 minutes. Kelly’s Pizzeria has a champion pizza eater named James who can eat 3 slices in 11⁄2 minutes. Who can eat more pizza in 1 minute?
Use a number line to show the difference between the amounts of pizza eaten by the two competitors in one minute.
pls help i really need this answer
Using number line, the difference in the amount of Pizza they ate is 0.75
What is the difference between the amounts of pizza eaten by the two competitors in a minute?To compare the amounts of pizza eaten by Sandy and James in 1 minute, we need to first calculate how many slices they eat in 1 minute.
Sandy can eat 6.5 slices in 2 minutes, which means she can eat 6.5/2 = 3.25 slices in 1 minute.
James can eat 3 slices in 1.5 minutes, which means he can eat 3/(1.5/2) = 4 slices in 1 minute.
Therefore, James can eat more pizza in 1 minute than Sandy.
To show the difference on a number line, we can mark 3.25 and 4 on the line, and subtract 3.25 from 4 to get the difference:
0 1 2 3 4
|---------|---------|---------|---------|
Sandy: 3.25
James: 4
Difference: 0.75
So the difference between the amounts of pizza eaten by James and Sandy in 1 minute is 0.75 slices.
Learn more on number line here;
https://brainly.com/question/12399107
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Select the correct answer.
Which graph represents this equation?
5y = x + 5
Answer: the graph that passes through 0,1
Step-by-step explanation:
y=1/5x+1
-2/9×-5/3
As a fraction...?
Tom read 240 pages of a book containing 360 pages. What fraction of the book did he read?
PLS simplify the answer!!
Answer:
2/3
Step-by-step explanation:
360 - 240 = 120
120 x 3 = 360
if 120 is 1/3 of 360, then 240 is 2/3 of 360
(disregard the zeros you don't need them)
Adele mows lawns in her neighborhood each weekend to save money for college.She uses her parents lawn mower,but is responsable for buying gas and other supplies she’ll need.The table below shows her profit after the first two lawns she moved last weekend.Adele charges the same amount of every lawn she mows.Select the function that models the relationship between her profit and the number of lawns she mows.
Answer:
P = 25m - 15
Step-by-step explanation:
Kindly find attached the table of values for your reference.
Step one:
given data
let us set up the coordinate using the value of p and m
p=35
p1=10
m=2
m1=1Tthe cordinate is (p1,p),(m1,m)= (y1,y),(x1,x)
(1,10), (2, 35)
the slop is given as, slope m = (p- p1)/(m - m1)
m=(35-10)/(2-1)
m = 25
from the equation of line y=mx+c
y = 25x + c
10 = 25(1) + bc
c= -15
y = 25x - 15
in term of m and p we have P = 25m - 15
PLEASe HELP ASAP!!!! Christine found a sweater at Nordstrom that was priced at $72.00. She noticed there was a sign that said "All sweaters are 20% off today. How much was the sweater before tax?
a
$57.60
b
$96.40
c
$70.56
d
$56.70
Drag the tiles to the correct boxes to complete the pairs. Match the values based on parallelogram ABCD, shown in the figure. length of value of m∠DAB value of 56 arrowRight 4 arrowRight 44 arrowRight 2 arrowRight
Answer:
56 ---> m< DAB
4 ---> length of line BC
44 ---> value of y
2 ---> value of x
Step-by-step explanation: edmentum test answer
The length of BC is 4 units, the value of y is 44, a measure of the angle DAB is 56 degrees, and the value of x is 2.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Parallelogram ABCD
From the figure:
6 - x = x + 2
2x = 4
x = 2
Length of BC = 6 - x = 6 - 2 = 4 units
12 + y = 100 - y
y = 44
Angle DAB = 100 - 44 = 56 degrees
The value of x = 2
Thus, the length of BC is 4 units, the value of y is 44, a measure of the angle DAB is 56 degrees, and the value of x is 2.
Learn more about the parallelogram here:
brainly.com/question/1563728
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In a survey of 2100 people who owned a certain type of car,735 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
35%
Step-by-step explanation:
the percent is given by the ratio 735 / 2100 = 7/20 = 0.35
which in percent form is 35%
What is the length of the radius, /?
O 8 units
O 10 units
O 12 units
O 16 units
Answer:
10
Step-by-step explanation:
ive done this before =)
