Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p: n = 195, x = 162; 95% confidence.a. 0.788 < p < 0.873.
b. 0.789 < p < 0.873.
c. 0.778 < p < 0.883.
d. 0.777 < p < 0.884.

Answers

Answer 1

Answer:

c. 0.778 < p < 0.883.

Step-by-step explanation:

The formula for confidence interval for proportion =

p ± z score × √p(1 - p)/n

p = x/n

n = 195, x = 162

z score for 95% confidence Interval = 1.96

p = 162/195

p = 0.8307692308

p ≈ approximately equal to = 0.8308

0.8308 ± 1.96 × √0.8308 × (1 - 0.8308)/195

0.8308 ± 1.96 ×√0.8308 × 0.1692/195

0.8308 ± 1.96 × √0.0007208788

0.8308 ± 1.96 × 0.0268491862

0.8308 ± 0.052624405

Confidence Interval

= 0.8308 - 0.052624405

= 0.778175595

Approximately = 0.778

= 0.8308 + 0.052624405

= 0.883424405

Approximately = p

0.883

Therefore, the confidence interval for this proportion = (0.778, 0.883) or option c. 0.778 < p < 0.883


Related Questions

02.01)Which is the ratio of the number of months that begin with the letter J to the total number of months in a year? 12 to 3 3 to 9 9 to 12 3 to 12 HELP!!! FOR MY MATH TEST

Answers

Answer:

3 to 12

Step-by-step explanation:

3 months (January, June, July) and 12 monthes

Answer: the answer is 3 to 12

Step-by-step explanation: hope this will help

y varies inversely with x. If y = 5 when x = 60, find y when x = 150
pre cal

Answers

Answer:

y = 2  when x = 150

Step-by-step explanation:

Inverse variation is

xy = k

5*60 = k

300 = k

xy = 300

150y = 300

Divide by 150

150y/150 = 300/150

y = 2

How do you do these questions? With step by step instructions please

Answers

Answer:         n = 3                                              n = 4                

               Upper Sum ≈ 3.41                      Upper Sum ≈ 3.25

               Lower Sum ≈ 2.15                      Lower Sum ≈ 2.25

Step-by-step explanation:

You are trying to find the area under the curve.  Area = height x width.

Height is the y-value at the given coordinate --> f(x)

Width is the distance between the x-values --> dx

n = 3

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3

So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9

f(1/3) =  1 + (1/3)² = 1 + 1/9 --> 10/9

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/3}          f(-1) = 2                   f(-1/3) = 10/9

{-1/3, 1/3}        f(-1/3) = 10/9           f(0) = 1   (vertex lies in this interval)

{1/3, 1}             f(1) = 2                   f(1/3) = 10/9

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]

*****************************************************************************************

n = 4

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)

So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4

f(0) = 1 + (0)² = 1

f(1/2) =  1 + (1/2)² = 1 + 1/4 --> 5/4

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/2}          f(-1) = 2                   f(-1/2) = 5/4

{-1/2, 0}          f(-1/2) = 5/4            f(0) = 1  

{0, 1/2}           f(1/2) = 5/4             f(0) = 1

{1/2, 1}            f(1) = 2                   f(1/3) = 5/4

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]

When you woke up this morning, the temperature was -5.8°C. At noon, the temperature was 2.9°C. Which expression and statement describes the situation?

Answers

Answer:

-5.8<2.9

Step-by-step explanation:

What is the measure of r

Answers

130 degrees

360-100=260
260/2=103

Answer:

The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°

CAN SOMONE PLEASE HELP ME ASAP PLEASEEE!!!​

Answers

Answer:

The yellow polygon is the scaled version of the red one (scaled by 3×), so the variable w = 9

Answer:

9

Step-by-step explanation:

The similarity ratio is 4/x = z/9 = 2/6 = 3/w = y/15

2/6 = 3/w cross multiply expressions 2w = 18 and w = 9

A bag contains 6 RED beads, 3 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?

Answers

Answer:

17/20

Step-by-step explanation:

Total no. of beads = 6 + 3 + 11 = 20

We need RED or GREEN bead .

So no. of beads needed = 6 + 11 = 17

So probability of getting GREEN or RED beads = 17/20

do all sets have subsets?

Answers

Answer:

yes

Step-by-step explanation:

Can someone plz tell me if I’m right?

Answers

Answer:

Step-by-step explanation:

Since x is used a lot as a variable in algebra, I would use another symbol for multiplication. Though if your teacher requires you to use x as a multiplication symbol, then keep it as is. I use the asterisk symbol

Example: 2 times 3 = 2*3

------------------------------------------

For problem 2, you have the parenthesis in the wrong spots. Saying "the sum of four plus five" means we have 4+5 as you'd expect. Then you multiply that group with 2. So you'd really have (4+5)*2

How is this different from 4+5*2 back in problem 1? It comes down to how the order of operations handles things. To evaluate 4+5*2, we multiply first, then add. So we have 4+5*2 = 4+10 = 14

With the other expression, we add first because it is in the parenthesis block. Afterward we multiply the values to get (4+5)*2 = 9*2 = 18

Amy, Ray, Kim, and Jamal are on a trivia team. They gain points for correct answers
and lose points for incorrect answers. During the contest, Amy gains 3 points, Ray loses
4 points, Kim loses 2 points, and Jamal gains 5 points. How many points does the team
have at the end of the contest?

Answers

Answer:

2 points

Step-by-step explanation:

0+3-4-2+5=2 points

Glados
spent the day at the mall, First, she bought
three bikes for $10 each. Later, she found 22
dollar bills. Write the total change
an integer.
to Glado's
funds as an integer

Answers

Answer:

8

Step-by-step explanation:

Find g(-2) + h(4) if g(x)= 5-2x and h(x) = - x2 pls help

Answers

Answer:

-7

Step-by-step explanation:

g(x)= 5-2x and h(x) = - x^2

g(-2) + h(4)

First find g(-2)

g(-2) = 5 -2(-2) = 5 +4 = 9

Then find h(4) = - 4^2 = -16

g(-2) + h(4) = 9-16 = -7

Answer:

-7

Step-by-step explanation:

Substitute -2 into g(x) equation,

g(x) = 5 - 2x

g(-2) = [5 - 2(-2)] = 9

Substitute 4 into h(x) equation,

h(x) = -x^2

h(4) = [-(4)^2] = -16

Therefore,

g(-2) + h(4) = 9 + (-16) = -7

Emma and Clair are planning to sell lemonade on their street. They have two recipes to choose from. Emma’s recipe calls for the juice of 5 lemons and 2 cups of water. Clair’s recipe calls for the juice of 2 lemons and 1 cup of water. Why will the first recipe taste more “lemony”?

Answers

Answer:

Emma's recipe will be more lemony because

5/2=2.5

2/1=2

Step-by-step explanation:

Answer:

The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.

Step-by-step explanation:

Sample Answer

The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.

|x______ | = _______

x = __________ (smaller number here)

x = _______ (larger nember here)

Blank 1:
Blank 2:
Blank 3:
Blank 4:

Answers

Answer:

[tex]|x - 85| = 12[/tex]

[tex]x = 73 \ (smaller\ number )[/tex]

[tex]x = 97 \ (larger \ number )[/tex]

Step-by-step explanation:

From the question we are told that

  The  grade is  [tex]k = 85\%[/tex]

   The  variation is  [tex]v = 12 \%[/tex]

Generally the absolute value equation is mathematically represented as

        [tex]|x - 85| = 12[/tex]

=>  [tex]x -85 = \pm 12[/tex]

So

    [tex]x = 85 + 12[/tex]

    [tex]x = 97 \ (larger \ number )[/tex]

And

     [tex]x = -12 + 85[/tex]

=>  [tex]x = 73 \ (smaller\ number )[/tex]

T is the midpoint of SU, ST = 8x + 11 and TU = 12x-1, find the value of x.

Answers

Answer:

x = 3

Step-by-step explanation:

mid point means it bisects the segment into two equals halfs meaning

ST = TU

8x + 11 = 12x - 1

8x + 12 = 12x

12 = 4x

3 = x

Point R is on line segment QS. Given RS = 13 and QS = 20, determine the length of QR

Answers

Answer:

Length of QR = 7

Step-by-step explanation:

20 - 13 = 7

I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me​

Answers

Answer:

(√2 + √6)/4.

Step-by-step explanation:

Use the addition formula

sin (A+ B) = sinAcosB + cosAsinB

sin (7pi/12) =  sin( 3pi/12 + 4pi/12)

= sin(pi/4 + pi/3) =  sin pi/4 cos pi/3 + cos pi/4 sin pi/3

= 1/√2 * 1/2 + 1/√2 * √3/2     (using the 45-45-90 and 30-60-90 triangles)

= 1 / 2√2 + √3/2√2

=   √2/4 + √6/4

= (√2 + √6)/4

(!20 POINTS PLEASE HELP!) The students in a class are randomly drawing cards numbered 1 through 28 from a hat to determine the order in which they will give their presentations. Find each probability. Solve each problem below 1. P(13) 2. P(less than 14) 3. P(not 2 or 17)

Answers

Since there is 28 cards, the chance of drawing 1 card will be [tex]\frac{1}{28}[/tex]

Therefore, [tex]P(13)=\frac{1}{28}[/tex].

There are 13 numbers less than 14 and greater than 0.

Therefore [tex]P(>14)=\frac{13}{28}[/tex]

There are 26 numbers that are not 2 or 17.

Therefore [tex]P(\neq 2,17)=\frac{26}{28}=\frac{13}{14}[/tex]

Hope this helps.

頑張って!

Probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

What is Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur

Given,

Total number of card = 28

Probability = Number of favorable outcome / Number of total outcome

Probability of picking 13 = [tex]\frac{1}{28}[/tex]

Probability of picking a card less then 14 = [tex]\frac{13}{28}[/tex]

Probability of not picking 2 or 17 = [tex]\frac{26}{28}=\frac{13}{14}[/tex]

Hence, the probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

Learn more about Probability here

https://brainly.com/question/11234923

#SPJ2

what is -3.5+(-4.9)=?What is the answer please?

Answers

Answer:

The answer is  -8.4

Bolts are packed into bags at a factory. Each bag should have 25 bolts in it but a bad with 22 or 28 is acceptable. Formulate an absolute value equation that could be used to solve for the minimum and maximum number of bolts in a bag.
|x____ | = ______
x = _____(smaller number here)
x = ________(larger number here)

Blank 1:
Blank 2:
Blank 3:
Blank 4:

Answers

Answer:

Absolute value equation is; |x - 25| ≤ 3

Minimum number of bolts is 22 while Maximum number of bolts is 28

Step-by-step explanation:

We are told that;

Each bag should have 25 bolts in it but 22 or 28 is acceptable.

Since 22 or 28 is acceptable, it means the allowable error is ±3.

Thus, if x is the number of bolts in the bag, the absolute value equation would be;

|x - 25| ≤ 3

Minimum number of bolts is 22 while maximum is 28

A factory worker can produce 28 toys in an eight hour day If there are 42 workers in total how many toys are produced every hour ​

Answers

Answer:

147 toys

Step-by-step explanation:

for 1 person, 28toys/8hours = 3.5toys/ 1hour

for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour

~Hope it Helps!~

d) 256 chocolates are distributed among the students of class 5.
If the number of chocolates obtained by each students is the same
as the number of students in the class, find the number of students
in the class?​

Answers

Answer:

16

Step-by-step explanation:

Let x be the number of chocolates obtained by each student

Since the number of chocolates obtained by each student = the number of students in the class, then, number of students in the class = x

256/x = x

Multiply both sides by x

256 = x × x ( x squared)

Multipy powers raised on both sides by 1/2

X = 16

A plane is a _____ figure

Answers

Answer:

bold

Step-by-step explanation:

hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd

A plane is a two dimensional figure.

use the values in the table to determine the slope.

Answers

Answer:

-3/2

Step-by-step explanation:

Take two points from the table and use the slope formula

m= (y2-y1)/(x2-x1)

   = ( 19 - 13)/ ( -4 - 0)

   = 6/-4

   = -3/2

Students in a large statistics class were randomly divided into two groups. The first group had a midterm exam that was printed on canary paper while the second group had the exam printed on pale green paper. The exam scores of the two groups were then then compared.This experiment was not blind because:_______a. Students were allowed to keep their eyes open while taking the exam.b. The exam was too long.c. The students knew whether or not music was playing while they were taking the exam.d. Some of the students did not study for the exam.e. Students were randomized into the two groups.

Answers

Answer:

e. Students were randomized into the two groups.

Step-by-step explanation:

alex buys six equally priced candy bars for $9:00 what is the unit rate?

Answers

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]

Now we will put the values into the above formula

[tex]= \frac{\$9:00}{6}[/tex]

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

A device has a constant failure rate with a MTTF of 2 months. One hundred of the devices are tested to failure. (a) How many of the devices do you expect to fail during the second month

Answers

Answer: the number of devices expected to fail during the second month is 24

Step-by-step explanation:

Given that

The device has a constant failure rate with MTTF of 2 months.

As the device has constant failure rate so it has exponential failure distribution

f(t) = λe^-λt

Here MTTF = 1/ λ

so  λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question,  Number of devices = 100

E( 1 < x < 2) = E ( x < 2) - E (x < 1)

so E(x < X) can be calculated with λ  = 0.5 Months⁻¹ will be calculated as the failure function

f(x) = λ exp ( - λ×t) for t > 0

F (x>0) = 1 - exp( - λx)

so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)

E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934

so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387

so the number of devices expected to fail during the second month is;

100 × 0.2387 = 23.87 ≈ 24

Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?

Answers

3 tests at 75% each = 3 x 75 = 225 total points

First two tests = 79 + 84 = 163

Third test needs to be at least: 225 - 163  = 62%

So any score less than 62 would get you into trouble.

Write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 in this order and insert '+' or '-' between them to get the result 3? Please Help

Answers

Answer:

0 - 1 - 2 + 3 - 4 + 5 - 6 +7 - 8 + 9 = 3

Step-by-step explanation:

Given the following formula, solve for I.
P =
2(1 + b)

Answers

Answer:  [tex]l=\dfrac{P}{2}-b[/tex]

Step-by-step explanation:

P = 2(l + b)

Divide both sides by 2:

[tex]\dfrac{P}{2}=l+b[/tex]

Subtract b from both sides:

[tex]\dfrac{P}{2}-b=l[/tex]

Note: You can also multiply b by  [tex]\frac{2}{2}[/tex] if you want the left side to be one fraction.

[tex]\dfrac{P}{2}-\bigg(\dfrac{2}{2}\bigg)b=l\\\\\\\dfrac{P-2b}{2}=l[/tex]

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