A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05. A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated.
(a) What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.)
(b) Is the sampling distribution of p approximately normal for random samples of size n 100? Explain.
i. The sampling distribution of p is approximately normal because np is less than 10.
ii. The sampling distribution of p is approximately normal because np is at least 10.
iii. The sampling distribution of p is not approximately normal because np is less than 10
iv. The sampling distribution of p is not approximately normal because np is at least 10
v. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10.

Answers

Answer 1

Answer:

a) The mean is 0.05 and the standard deviation is 0.0218.

b)  v. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10.

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].

If [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the sampling distribution of the sample proportion p will be approximately normal.

Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.

This means that [tex]p = 0.05[/tex]

A random sample of n = 100 people

So [tex]n = 100[/tex]

(a) What are the mean and standard deviation of the sampling distribution of p?

Mean [tex]\mu = p = 0.05[/tex]

Standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{100}} = 0.0218[/tex]

The mean is 0.05 and the standard deviation is 0.0218.

(b) Is the sampling distribution of p approximately normal for random samples of size n 100? Explain.

[tex]np = 100*0.95 = 95 > 10[/tex]

[tex]n(1-p) = 100*0.05 = 5 < 10[/tex]

As n(1-p) < 10, it is not approximately normal, option v.


Related Questions

please answer them! be quick if you can, thank you.

Answers

Answer:

Question one = 35a - 15

Question two = 9

Step-by-step explanation:

Distributive property means to multiply all the numbers inside the parenthesis

by the outside number. 5 x 7a equals 35a and 5 x 3 = 15.

35 x 9 - 315 - 15 = 300

A = 9

points: here answer 3b+10

Answers

Answer:

3b+10

Step-by-step explanation:

The expression is not factorable with rational numbers.

3b+10

Question in link. Please help :(

Answers

Answer:

The median

Step-by-step explanation:

It uses all the added numbers as one

The three side lengths of a triangle are given. Which triangle is a right triangle?

hopefully the text is ok :-)

Answers

Answer:

Triangle A

Explanation:

This isn't really an explanation, but I don't really know how to explain. The other answers just aren't correct (They aren't right triangles).

Due today! Why did the "Martian" need a special suit to visit Earth?

Answers

Answer:

But Mars has no magnetosphere, and its atmosphere is over 100 times thinner than Earth's atmosphere. The trip to Mars and the stay on Mars will mean extended radiation exposure. Astronauts will need special habitats, suits, and machines that will protect them from radiation, which otherwise could cause cancer.

Step-by-step explanation:

Please help! Like please.

Answers

The answer is letter H

please look at my last couple questions!! 50% of my grade
NO LINKS​

Answers

D. All other choices are wrong

Can y’all help me solve this?

Answers

Do you have to give me the whole graph lol

Kathryn is 1.6 meters tall. Convert her height to feet. Round to the nearest tenth.

Answers

Answer:

1.6 m = 5.3 ft

0.8km need to be convert into hour an minute please help

Answers

Answer:

It is not possible

Step-by-step explanation:

Required

Convert 0.8km to hours and minutes

One of the condition for a successful conversion is that: only units of the same metric can be converted.

i.e.

Meters can be converted to feet (they both measure distance)

Days can be converted to years (they both measure time)

Pounds can be converted to grams (they both measure weight)

But in the given question, you attempt to convert from distance to time.

This is not possible, because time and distance are different measurements

if f(x) = 2x+6 and g(x) = x(3) , what is (g0f)(0)

Answers

Answer:

(g0f)= (2x0+6 x 0x3)= 8x3= 24

Step-by-step explanation:

I'm not sure

:) sorry

3) Divide x3 + 4x2 – 3x – 12 by (x + 4)

Answers

Answer:

Factor the numerator and denominator and cancel out the common factors.

x ^2 − 3 is your final answer.

Step-by-step explanation:

Hope that this helps you out! :)  

If you have any questions please put them in the comment section below this answer.  

Have a great rest of your day/night!  

Please thank me on my profile if this answer has helped you.

I am not sure how to solve these equations. Can someone please help me?

Answers

Answer: 1. 1.14142842 (sorry this is what i got)

               2.  -13.14142842

Step-by-step explanation:

2 Which expression shows the quotient of 6 and p?
A 6xp
с px6
в 6+ р
D p +6

Answers

Probably d is there is

PLS HELP DUE VERY SOON
3. Consider the following box plot.

(a) Find the interquartile range.

(b) What percent of values is included in the interquartile range?

Answers

Answer:

a) Interquartile range= upper quartile- lowwr quartile

= Q3- Q1

= 4.75-2.25

= 2.50

b) ( 2.5 ÷ 6 ) × 100

= 41.67%

Answer:now you can give other guy brainliest.

Step-by-step explanation:

CAN SOMEONE PLEASE ANSWER THIS QUICKLY I DONT GOT TIME​

Answers

Answer:

6) 5(1/3)

7) 5(1/3)

8) 3(3/5) or 18/5

because answer were cut off

Answer:

7) 5 [tex]\frac{1}{3} \\[/tex]

8) 5 [tex]\frac{1}{3}[/tex]

9) 3 [tex]\frac{3}{5}[/tex]

hope it is right, just use your calculator

∠A and \angle B∠B are complementary angles. If m\angle A=(x+10)^{\circ}∠A=(x+10)

and m\angle B=(3x+28)^{\circ}∠B=(3x+28)

, then find the measure of \angle B∠B.

Answers

Answer:

x + 10 + 3x + 28 = 90

4x = 52

x= 13

Step-by-step explanation:

Angle B = 67

which expression is 1/2 as large as 486-466

Answers

Answer: 20-10

Step-by-step explanation: 486-466 is 20. Half of 20 is 10. Any expression that equals ten is 1/2 as large as 486-466.

The expression is 1/2 as large as 486-466 is with the data 10.

What is fraction?

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Let us understand this concept using an example. The following figure shows a pizza that is divided into 8 equal parts. Now, if we want to express one selected part of the pizza, we can express it as 1/8 which shows that out of 8 equal parts, we are referring to 1 part.

Given:

Class = 486 - 466

We have given a class whose upper limit = 486

and, lower limit = 466

the range or difference between class

=486 - 466

=20

Thus, the 1/2 of range is 10.

Hence, expression is 1/2 as large as 486-466 is with the data 10.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ2

The distance around a triangle is 36 centimeters. If two sides are equal and the length of the third side is 14 centimeters, what is the length of each of the other two sides?

Answers

Length of unknown side = x

36 = 14 + 2x

Subtract 13 from both sides

22 = 2x

Divide by 2 on both sides to isolate for x

11 = x

11 cm

Raul recibió un bono de $750, el que era 5% de su salario anual . Su sueldo anual es de ?

Answers

Answer: 375

Step-by-step explanation:

plz help me I'm timed!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!​

Answers

Answer:

Answer is C. 9

Step-by-step explanation:

It is basically the same thing as 12-3 and that's equal to 9. It's 9 my man

Edge Precalculus End Behavior of Limits

Answers

Answer:

ereee

Step-by-step explanation:

Answer:

c.

g(x)=-3/x

Step-by-step explanation:

In a company's first year in operation, it made an annual profit of $322,000. The
profit of the company increased at a constant 21% per year each year. How much
total profit would the company make over the course of its first 26 years of operation,
to the nearest whole number?

Answers

Answer:

Since the annual profit for the FIRST YEAR is $322,000 and it increases 21% every year for 26 years, you do so to find the answer to the question.

Step-by-step explanation:

21% per year

26 years

21 x 26 = 546

Now you have to find 546% of 322,000 and add that to 322,000.

546% of 322,000 is 1,758,120.

hope this helped!

Answer:

$216,265,829

Step-by-step explanation:

To find the sum of a geometric series we use the following equation

[tex]a*\frac{1-r^n}{1-r}[/tex]

we have

[tex]322000*\frac{1-1.21^{26}}{1-1.21}\\\\322000*671.633=216265829[/tex]

Help me plzzzzz euebdmso

Answers

True, true, false, false

2(3b-1)=40
Simplify.

Answers

Answer:b=7

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(3b−1)=40

(2)(3b)+(2)(−1)=40(Distribute)

6b+−2=40

6b−2=40

Step 2: Add 2 to both sides.

6b−2+2=40+2

6b=42

Step 3: Divide both sides by 6.

6b/6=42/6

b=7

Is this a Percent Increase or Decrease Problem?
Shaleka had a 10%-off coupon and paid $36 for pair of
jeans.

Answers

Answer:

Percent Decrease

Please mark as brainliest for further answers :)

The growth in per share FCFE of FOX, Inc. is expected to be 10%/year for the next three years, followed by a growth rate of 5%/year for two years; after this five year period, the growth in per share FCFE is expected to be 3%/year, indefinitely. The required rate of return on FOX, Inc. is 12%. Last year's per share FCFE was $1.8. What should the stock sell for today?

Answers

Answer: $25.46

Step-by-step explanation:

Year 1 FCFE = 1.8 * (1 + 10%) = $1.98

Year 2 FCFE = 1.98 * 1.1 = $2.18

Year 3 FCFE = 2.178 * 1.1 = $2.40

Year 4 FCFE = 2.3958 * 1.05 = $2.52

Year 5 FCFE= 2.51559 * 1.05 = ‭2.64

Terminal Value = (2.64 * 1.03) / (12% - 3%)

= $30.21

Now discount all these cashflows to find the value:

= (1.98 / 1.12) + (2.18 / 1.12²) + (2.40 / 1.12³) + (2.52 / 1.12⁴) + (2.64 / 1.12⁵) + (30.21 / 1.12⁵)

= $25.46

help pleaseee !!! im stuck

Answers

9514 1404 393

Answer:

102 cm²232 in²40.46 ft²480 mm²

Step-by-step explanation:

The first three cuboid prisms all use the same area formula:

  A = 2(LW +H(L+W))

__

1. A = 2(3·3 +7(3+3)) = 2(9 +42) = 102 . . . cm²

2. A = 2(2·8 +10(2 +8)) = 2(16 +100) = 232 . . . in²

3. A = 2(4.9·3 +0.7(4.9 +3)) = 2(14.7 +5.53) = 40.46 . . . ft²

__

4. The area of this prism is the total of the area of the two triangular bases  and the areas of the rectangular faces. For triangle legs a, b and hypotenuse c, and prism depth d, the area formula can be written as ...

  A = ab +d(a+b+c)

  A = (8 mm)(15 mm) +(9 mm)(8 mm + 15 mm + 17 mm)

  A = (120 +9(40)) mm² = 480 mm²

I need help, I’ll reward points + brainalist (btw I need help with 12, help a guy out please don’t just say “look at the link”)

Answers

Answer:

B (2)

Step-by-step explanation:

The formula for circumference of a circle is C=2piR

Replace R with 2

C=2pi(2)

C=12.5664

Formula for area of a circle is A=piR^2

A=pi(2)^2

A=12.5664

What is the answer to this question

Answers

The best answer from the choices provided is option B) 56.

Step-by-step explanation: Simply subtract 34 from 90.

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