Solving for a Confidence Interval: Algebra 2 points possible (graded) In the problems on this page, we will continue building the confidence interval of asymptotical level 95% by solving for p as in the video. Recall that R1,…,Rn∼iidBer(p) for some unknown parameter p , and we estimate p using the estimator p^=R¯¯¯¯n=1n∑i=1nRi.
As in the method using a conservative bound, our starting point is the result of the central limit theorem:
In this second method, we solve for values of P that satisfy the inequality volves penat che non esito para polcomp R -P
To do this, we manipulate - ulate | " Vp(1-) 5 < 90/2 into an inequality involving a quadratic function App + Bp+C where A > 0, B, C la/2 into an inequality in depend on 13, 4a/2, and R. Which of the following is the correct inequality?
(We will use find the values of A, B, and C in the next problem.)
1. Ap^2 + Bp + C<0 where A >0.
2. Ap^2 + Bp+C>Owhere A >0.
Let P1 and P2 with 0 a. (P P2)
b. P

c. o

d. P2

e. o

Answer:

Step-by-step explanation:

1) The given inequality is

[tex]|\sqrt{n} \frac{(\bar R_n-p)}{\sqrt{p(1-p)} } |<q_{\alpha /2}| \\\\ \to(\frac{(\sqrt{n} \bar R_n-p)}{\sqrt{p(1-p)} })<q^2_{\alpha /2}[/tex]

[tex]\to n( \bar R _n - p)^2<p(1-p)q^2_{\alpha /2}[/tex]

[tex]\to n\bar R +np^2-2nR_np<q^2_{\alpha /2 p- q^2_{\alpha /2}p^2[/tex]

Arranging the terms  with p² and p, we get

[tex]p^2(n+q^2_{\alpha /2)-p(2n \bar R _n+q^2_{\alpha / 2})+n \bar R ^2 _n <0[/tex]

Hence, the inequality is of the form

Ap² + Bp + c < 0

2. A quadratic equation of the form

Ap² + Bp + c < 0 with A > 0 looks like

Check the attached image

The region where the values are negative lies between p₁ and p₂ ...

The p₁ < p < p₂

Which of the following is the slope of the line that passes through the points (-3,5) and (-3,-2)

Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75

if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
The product of 8 and a number is 96. Find the number.
Write an equation for the given conditions.

In the circle above, P is the center,​What is the value, in degrees, ​of θ?

Gordon​ Miller's job shop has four work​ areas, A,​ B, C, and D. Distances in feet between centers of the work areas​ are: A B C D A − 5 9 7 B − − 6 8 C − − − 11 D − − − − Workpieces moved per week between work areas​ are: A B C D A − 900 900 500 B − − 500 200 C − − − 600 D − − − − It costs Gordon ​$22 to move 1 work piece 1 foot.What is the weekly total material handling cost of the layout?

If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)

2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?​

When Ryan was born, he weighed 7 pounds.At 6 months, he weighed 11.2 pounds. Amanda weighed 6 pounds when she was born, and 12.9 pounds at 6 months. Which baby had a greater percent increase in weight? Explain

PLEASE HELP Last year Lenny had an annual earned income of $58,475. He also had passive income of $1,255, and capital gains of $2,350. What was Lenny’s total gross income for the year?
a.
$58,475
b.
$59,730
c.
$60,985
d.
$62,080


Please select the best answer from the choices provided

A
B
C
D

Can anyone help me with my homework ?
2x+3y=20
7x+2y=53

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1. Molly is trying to find a relationship between the largest angle and largest side of a triangle. She has drawn dozens of triangles, and measured their parts. She’s ready to make a conjecture. What kind of reasoning was Molly using? Explain how you know it’s that kind of reasoning.

11. Which step in the proof has a flaw?
Given AB=BC prove B is the midpoint of AC
IMAGE BELOW
A) Step 1
B) Step 3
C) No Flaw.
D) Step 2

4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty
members do not have a PhD. In the Department, the number of female faculty who do not
have a PhD is 10 more than the number of females who have a PhD. If a third of the male
faculty in the Department have a PhD, then what is the number of female faculty in the

The graph shows the amount of protein contain in a certain brand of peanut butter. Which statement describes the meaning of the point (6, 30) on the graph?

A.) There are 6 g of protein per tablespoon of peanut butter.

B.) There are 30 g of protein per tablespoon of peanut butter.

C.) There is 6 g of protein in 30 tablespoons of peanut butter.

D.) There are 30 g of protein in 6 tablespoons of peanut butter.

no guess please explain

B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.​

The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it is reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?

A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.

Simplify
20x over 70x

a circle with circumference 20 has an arc at 72 central angle. what is the length of the arc

A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building?
(Hint: Draw a picture and Set up a proportion)

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve

A payday loan store charges $40 for a one month loan of $600. What’s the annual interest rate equivalent to?

A machine produces 576 units in 18 hours at this rate how many will it produce in 28 hours

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the​ mean, or between 96.36degreesF and 100.02degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degrees​F?

Convert 88 ounces to pounds.
A.0.18 pounds
B.5.5 pounds
C.1408 pounds

The m∠ABC = (10x-5)°and m∠CBD=35°. If the angles are supplementary, find the value of x.

can someone please help meee!???

Please everyone help me!

A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle