1. If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)
2. Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 4% at the 95% confidence level, how many randomly selected teenagers must we survey?

Answers

Answer 1

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.

Answer 2

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


Related Questions

The graph of an equation with a negative discriminant always has which characteristic?
OO
no x-intercept
no y-intercept
no maximum
no minimum

Answers

No x intercept because there is no solution

pls solve this and you get the points i'm a lil high right now

Answers

Answer:

solve for V= pier^/3

solve for R=Square root3Vpie over pie

Step-by-step explanation:

V=multiply 1/3(pier^2)

R= Take root of both sides and solve

Answer:

dividing by a fraction (1/3) is equivalent to multiplying by its inverse (3)

3+%2A+v+%2F+%28pi+%2A+r%5E2%29 = h

Step-by-step explanation:

Which equation has the correct sign on the product?
A 45(-4)=180 B 13•3= -39
C (-8)(-8)= -64 D (-18)4 = -72​

Answers

answer:

the answer is a

Answer is D because (-18)4 equals -72.... it’s right.

It takes andre 4 minutes to swim 5 laps. At this rate heswims how many laps per minute.

Answers

Answer: It takes him 1 minute and 25 seconds

Step-by-step explanation:

5 divided 4

4 times 1 = 4

5-4=1

put the decimal and make 1=10                           Ans.: 1.25

4 times 2 = 8

10-8=2

put the 0 = 20

4 times 5 =20

20-20=100

it takes Molly 0.25 hours to drive to school. her route is 16 km long. what is Molly's average speed on her drive to school?​

Answers

Answer:

64

Step-by-step explanation:

16 divided by 0.25 gives you 64 .... welcome

Answer:

64 km/h

I answered it correctly on a mid term

13. What is the value of x?
t
(2x +40)
(x +90°
С
D
A. 25
B. 50
C. 75
D. 85

Answers

9514 1404 393

Answer:

  B.  50

Step-by-step explanation:

The alternate interior angles at transversal t across parallel lines AB and CD will be congruent.

  2x +40 = x +90

  x = 50 . . . . . . . . . . . subtract x+40

The value of x is 50.

_____

Check

2x+40 = 2×50 +40 = 140

x+90 = 50 +90 = 140 . . . . so the obtuse angles are congruent, as they should be

___

Additional comment

The lines AB and CD are not shown as being parallel. We have to assume they are, or we cannot work the problem.

What’s the unit rate for Tegan?

Answers

Answer:

The unit rate is 16

The unit rate is 16 I think

11. Find the product of (4x-5) and (2x+7) in simplest form.

Answers

8x^2 + 18x - 35


(4x - 5)(2x + 7)

8x^2 + 28x - 10x - 35

8x^2 + 18x - 35

#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%

Answers

It will be 25%

Step-by-step explanation:

In March it rained 8.23 inches. It rained 5.96 inches less in April than in March.
How much did it rain in April?

Answers

It rained 2.27 inches in April.

Which ordered pair is a solution to the equation below? 3x + 2y = 10
Question 1 options:

(4, 0)

(6, -4)

(-1, 4)

Answers

Answer:

(6,-4)

Step-by-step explanation:

I have tried replacing each option with x, y in the equation.

Let's replace (6, -4) with x and y

3x+2y=10

3(6)+2(-4)=10

3(6)= 18 2(-4)= -8

18+(-8)=10

in other words:

18-8=10

The statement is true, so the correct answer is:

(6, -4)

Help i need the answer now please!

Answers

Answer:

no

Step-by-step explanation:

No , Have Ah Nice Day

Help me pleaseeeeeeeeeeeeeeeeee

Answers

Answer:A. 4 13/24Hope this helps!!
The answer is 4 13/24

There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?

Answers

I need help to I’m struggling at math

You start an account with $2,500 and an annual interest rate of 6.5% compounded yearly. How much is in the account after 7 years?

I need an expression and a solution​

Answers

I'm pretty sure it's this:

Answer:

y=a( 1+  r/n)^ nt

growth is a= 2500     yearly is n= 1

y= 2500( 1+ .065/1)^ 1.7  =   $3884.97

                                 

.
Determine the value of each of the following expressions

a.
25+310


b.
56−13


c.
45×78


d.
67÷34

Answers

a. 515
b. 43
c. 3510
d. 1.9705

a nursery sells kentucky bluegrass seed for $5.75 per pound and tall fescue seed for $4.50 per pound. the nursery sells a mixture of the two kinds of seed for $5.25 per pound. let k represent the amount of kentucky blue grass seed the nusery uses in in 5 pounds of the mixture

Answers

Answer:

[tex]k=3[/tex]

Step-by-step explanation:

Given that:

Per pound cost of kentucky bluegrass seed = $5.75

Per pound cost of tall fescue seed = $4.50

Per pound cost of mixture of seeds = $5.25

[tex]k[/tex] is the amount of kentucky blue grass.

Total amount of the mixture = 5 pounds

Therefore, amount of tall fescue seed = (5 - [tex]k[/tex]) pounds

To find:

The value of [tex]k[/tex].

Cost of [tex]k[/tex] pounds of kentucky bluegrass seed = [tex]\$5.75k[/tex]

Cost of (5 - [tex]k[/tex]) pounds of tall fescue seed = [tex]\$(5-k)4.50[/tex]

As per question statement:

[tex]5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds[/tex]

Amount of kentucky blue grass seed used = 3 pounds

Amount of tall fescue seed used = 5-3 = 2 pounds

Xavier's car used 4 gallons to travel 152 miles. How many miles can the car go
on one gallon of gas?

Answers

Answer:

1 gallon of gas= 38 miles

Step-by-step explanation:

152÷4= 38.

what type of angle is 2??
a. Alternate Exterior
b. Alternate Interior
c. Corresponding
d. Linear Pair
e. Same-Side Exterior
f. Same Side Interior
g. Vertical Angles
h. No Relationship

Answers

Answer:

Vertical Angles...............

FIRST ONE TO GET ME THE CORRECT ANSWER WILL WIN BRAINIEST

Answers

9514 1404 393

Answer:

  59 3/4

Step-by-step explanation:

The change from the opening price is ...

  -50 1/2 +110 1/4 = 60 -1/4 = 59 3/4 . . . change from opening price

The function
The function g(x) has a slope of —5/6. The value of g (x) is 5 when x is 6. Explain how the graph
of g(x) can be used to find the x-intercept. (2 points)
Item

Answers

You have slope and a point so it should be easy.
Set up equation [y-y1= m(x-x1)]
y-5 = -5/6(x-6)
And simplify.
Y=-5/6x +10

Then to find x intercept, plug in a 0 for y
0=-5/6x+10
-10=-5/6x. Subtract 10 from both sides.
-10/ -5/6 = x. Divide by -5/6 on both sides.

X=12

So the x intercept is 12 or (12,0)

-3- 2 1/3 please help me out

Answers

Answer:-2/3

-3-2 1/3

which is also

-3 -7/3

which is also

-9/3-7/3

which is

-2/3

The difference is -5 1/3


1. Find the value of k.
A. 17
B. 73
C. 118
D. 107

Answers

A i’m pretty sure 62-45

Answer:

Its B

Step-by-step explanation:

you have to add 45 and 62 to get 107 and then subtract 107 from 180

Hope this helps

pls mark brainliest

Graph the equation y=-x^2+12x-32y on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answers

use desmos ... that’s what i use for math

The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.

How to graph a quadratic function

By fundamental algebra theorem we need at least three no coplanar different points to graph quadratic functions. First, we determine 5 different points, then we pass the curve through the five points and finally we identify the roots and the vertex.

If we know that (- 16, - 480), (- 12, - 320), (- 8, - 192), (- 4, - 96), (0, - 32), then the graph of the quadratic function is shown in the image.

The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.

To learn more on quadratic functions: https://brainly.com/question/5975436

#SPJ2

Step 1:Choose the lowest common denominator

Find the sum of 1/5 and 7/10

The expression written in equation from with common denominator is______

The sum is___​

Answers

Answer:

-6/8 +5/8 and -1/8

Step-by-step explanation:

just got done doing it.

Determine the expression

Answers

trinomial and i believe its a degree of 4

I need to know for you to Awnser my question


Points and brainlest !!!

Answers

Answer:

id c hot  hf hdjhdw fhwjfehf v;e

Step-by-step explanation:

id c h

Answer:

2/3

Step-by-step explanation:

theres only 4 less than 5 out of 6 so the fractio is 4/6. 4/6 simplified is 2/3


If the ratio of the length of a rectangle to its width is
9/4 and it’s length is 18 cm, what is the width of the rectangle?

Answers

9514 1404 393

Answer:

  8 cm

Step-by-step explanation:

It is convenient to write the proportion with the unknown (width) on top:

  width/length = 4/9 = w/(18 cm)

Multiplying by 18 cm gives ...

  w = (18 cm)(4/9) = 8 cm

The width of the rectangle is 8 cm.

Answer:

The answer is 8.

Step-by-step explanation:

I did a test with this question on it.

This was the correct answer.

YOUR WELCOME!!! HOPE IT WAS HELPFUL :)

Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.

Answers

Answer:

i need a bad bleep

Step-by-step explanation:

addison rae


18
=
4
Convert the improper fraction to a mixed number.

Answers

Answer:

[tex]4\frac{1}{2}[/tex]

Step-by-step explanation:

In order to find the answer to this question you have to divide the numerator by the denominator.

[tex]\frac{18}{4}[/tex]

[tex]4\times4=16[/tex]

[tex]18\div4=4^2[/tex]

[tex]4\frac{2}{4}[/tex]

Reduce:

[tex]2\div2=1[/tex]

[tex]4\div2=2[/tex]

[tex]=4\frac{1}{2}[/tex]

Hope this helps.

Other Questions
How are prism and cylinders are alike ? What two subatomic particles add up to make the mass? What is the value of the function at x=2? How can you use spoken or written language to fight or advocate for an issue? In paragraph 3, the narrator says, "I knewfrom experience that this could only meanone thing." From this, the reader canunderstand thathighlight textA. the narrator needed his aunt's permissionto go on the tripB. his aunt would like to be a chaperone onthe tripC. the narrator's family has been in similarsituations beforeD. the narrator's mother is usually able toafford the things they need Which claim about the power of accomplishments does the author make in The Fish I Didnt Catch?AAccomplishments are worthy of boasting.BAccomplishments are deserving of credit.CAccomplishments speak for themselves.DAccomplishments aren't real until they're complete. What, exactly, is moving across the medium? Give the domain and range of the relation. Can someone help me with this only answer if you're sure. The volume of the large cube is 125 cubic inches. The volume of the small cube is 27 inches. What is the difference between the length of one side of the large cube and the length of one side of the small cube? Roger is studying how energy from the Sun changes to chemical energy in plants and to mechanical energy in animals. He is studying _____. quantum physics chemistry biology thermodynamics Connor bought 40 pencils for $0.35 each. Mara bought 70 pencils at the same price. How much more money did Mara spend? How did the ice age make the agricultural revolution possible ANSWER PLS OR NOTHING WILL HAPPEN What will happen if we increase the friction on a roller coaster?A. The speed of the roller coaster will increase.B. The speed of the roller coaster will decreaseC. The speed of the roller coaster will remain constant.D. The roller coaster will fly away Who did Abraham Lincoln appoint has the Commander of the Army of the Potomac? Which type of government is found most often in the world? PLEASE HELP ME ASAP??!Which of the following are valid names for the triangle below? Check all thatapply. Fill in the blank in the following sentence with the appropriate word(s) below.Lucie pense souvent _____.A. de Paries B. jouer du piano.C. sa grand-mreD. le Canada Will mark brainliest!! Please answer ASAP Will give extra points!!!Please let me know if the picture above answer is correct or not and tell me the right answer!Second question-Which linear equation can be used to represent a line parallel to the x axis that passes through the point (8,5) 1) y=5 2) y=x+83) y=x+5