Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99% confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?
a. 400.
b. 900.
c. 1,300.
d. 1,600.
e. 2,100.

Answers

Answer 1

Answer:

d. 1,600.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months.

This means that [tex]\sigma = 1.5[/tex]

Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

The sample size has to be n or larger. n is found when [tex]M = 0.1[/tex]. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 2.575\frac{1.5}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 2.575*1.5[/tex]

Multiplying both sides by 10

[tex]\sqrt{n} = 2.575*15[/tex]

[tex](\sqrt{n})^2 = (2.575*15)^2[/tex]

[tex]n = 1492[/tex]

So the sample size has to be at least 1492, which means that of the possible options, the smallest sample size is 1600, given by option d.

Answer 2

The sample size should be at least 1492, So the possible options, the smallest sample size is 1600, option D is the correct answer

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99% confidence interval for the average age at which children begin to walk will be constructed.

What is the margin of error?

The margin of error tells you how many percentages points your results will differ from the real population value.

[tex]M=z\frac{\sigma}{\sqrt{n} }[/tex]

We need to find our α level, that is the subtraction from 1 by the confidence interval for the average age divided by 2.

[tex]\alpha = \frac{1-0.99}{2}\\ =0.005[/tex]

Now, we need to find z which is 1-α

[tex]1-\alpha \\=1-0.005\\\rm z=2.575[/tex]

The margin of error M

[tex]M=z\frac{\sigma}{\sqrt{n} }[/tex]

Here, [tex]\sigma[/tex] is the standard deviation of the population.

n is the size of the sample.

So,

[tex]\rm M=z\frac{\sigma}{\sqrt{n} } \\\rm0.1=2.575\frac{1.5}{\sqrt{n} } \\\rm0.1\times\sqrt{n} =2.575\times{1.5}\\\rm\sqrt{n} =2.575\times{1.5}\\\rm(\sqrt{n} )^{2} =(2.575\times{1.5})^{2} \\\rm n=1492[/tex]

Hence, the sample size should be at least 1492, So the possible options, the smallest sample size is 1600, option D is the correct answer.

Learn more about the margin of error here:

https://brainly.com/question/6979326


Related Questions

According to survey​ data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a standard deviation of 3.1 inches. a. What percentage of men have arm spans between 66 and 76 ​inches? b. A particular professional basketball player has an arm span of almost 89 inches. Find the​ z-score for this​ person's arm span. What percentage of males have an arm span at least as long as this​ person?

Answers

Answer:

a) 89.97% of men have arm spans between 66 and 76 ​inches.

b) The z-score for this​ person's arm span is 5.68. 0% of males have an arm span at least as long as this​ person

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 71.4 inches and a standard deviation of 3.1 inches.

This means that [tex]\mu = 71.4, \sigma = 3.1[/tex]

a. What percentage of men have arm spans between 66 and 76 ​inches?

The proportion is the pvalue of Z when X = 76 subtracted by the pvalue of Z  when X = 66. The percentage is the proportion multiplied by 100.

X = 76

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{76 - 71.4}{3.1}[/tex]

[tex]Z = 1.48[/tex]

[tex]Z = 1.48[/tex] has a pvalue of 0.9306

X = 66

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{66 - 71.4}{3.1}[/tex]

[tex]Z = -1.74[/tex]

[tex]Z = -1.74[/tex] has a pvalue of 0.0409

0.9306 - 0.0409 = 0.8997

0.8997*100% = 89.97%

89.97% of men have arm spans between 66 and 76 ​inches.

b. A particular professional basketball player has an arm span of almost 89 inches. Find the​ z-score for this​ person's arm span. What percentage of males have an arm span at least as long as this​ person?

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{89 - 71.4}{3.1}[/tex]

[tex]Z = 5.68[/tex]

The z-score for this​ person's arm span is 5.68.

Z = 5.68 has a pvalue of 1

1 - 1 = 0

0% of males have an arm span at least as long as this​ person

The percentage of men who have arm spans between 66 and 76 inches is 89.97% and the percentage of males who have an arm span at least as long as this​ person is 0%.

Given :

According to survey​ data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a standard deviation of 3.1 inches.

a) The formula of z-score is given below:

[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]

where [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

When X = 66 the formula of z-score becomes:

[tex]\rm Z = \dfrac{66-71.4}{3.1}[/tex]

Z = -1.74

The p-value regarding the (Z = -1.74) is 0.0409.

When X = 76 the formula of z-score becomes:

[tex]\rm Z = \dfrac{76-71.4}{3.1}[/tex]

Z = 1.48

The p-value regarding the (Z = 1.48) is 0.9306.

Now, the percentage of men who have arm spans between 66 and 76 inches is:

= (0.9306 - 0.0409) [tex]\times[/tex] 100 %

= 89.97%

b) Now, at X = 89 the formula of z-score becomes:

[tex]\rm Z = \dfrac{89-71.4}{3.1}[/tex]

Z = 5.68

The p-value regarding the (Z = 5.68) is 1.

So, the percentage of males who have an arm span at least as long as 89 inches ​is:

= (1 - 1) [tex]\times[/tex] 100 %

= 0%

For more information, refer to the link given below:

https://brainly.com/question/13299273

What round 3\7 to is closest

Answers

how DO I DELETE THIS ANSWER

find tan C will mark branylis​

Answers

Answer:

i think26 and 10

Step-by-step explanation:

Answer:

c.  12/5

Step-by-step explanation:

With reference angle C

perpendicular (P)= 24

base(b) = 10

Then

Tan < C = p / b

Tan < C = 24/ 10

Tan < C = 12/5

Hope it helps :)

GUYS, I KNOW THIS IS A LOT BUT BECAUSE I HAD NO ELECTRICITY I WAS UNABLE TO DO IT AND NOW I'M BEHIND. PLS HELP! I'M RUNNING OUT OF POINTS!

Answers

Answer:

Hey! I'll only help with a few..

Step-by-step explanation:

2. 2c(7c+1)

3. The expression is not factorable with rational numbers.

4. 2x^3y^2(4-11 x^2y^4)

Hope this helps!

Have a nice day!♥

What four fractions can be made with the cards that have values less than 12

Answers

Answer:

4/8 3/6 5/10 2/4 6/12

Step-by-step explanation:

pls give me the crown pls

and i hope this helped you :)

Please tell me the letter of the answer

Answers

Answer:

C 37.5

Step-by-step explanation:

1 inch is 30 feet. so feet is 30 x [number of inches]. 30 x 1.25 = 37.5

Dara pinkston Recorded her house and expenses for a month of August mortgage payment was 347.90Insurance $17 Texas $84 electricity $64.40 phone service $33.50 fuel $98.25 water $17.44 in repairs $79.87 .Her monthly take-home pay is 2150 what’s her total money coast?

Answers

Answer:

the total monthly cost is $742.36

Step-by-step explanation:

The computation of the total monthly cost is shown below:

= Mortgage payment + insurance + taxes + electricity + phone service + fuel + water + repairs

= $347.90 + $17 + $84 + $64.40 + $33.50 + $98.25 + $17.44 + $79.87

= $742.36

Hence, the total monthly cost is $742.36

If a=.3 and b=.5, what is the value of a=b ?

Answers

Answer:

5.0/5.

Step-by-step explanation:

Answer:

3A = 5B A/B=5/3 (A + B) / B=(5+3) / 3 (A + B) / B=8/3 इसलिए सही उत्तर विकल्प B है।

Hope this helps

Step-by-step explanation:

Help im being timed.

Answers

Answer:

the answer is D

Step-by-step explanation:

Answer:

D. 6g

Step-by-step explanation:

ILL MARK BRAINLIEST!!! PLS HELP!!! A car purchased for $18,000 depreciates annually at a rate of 5%.
What will be the approximate value of the car in the 10th year?

Answers

Answer:

Step-by-step exlanation:

What you do is $18,000 x 5% which is 900 and then you do 900 x 10 = 9000!

20% of the students in the school are in kindergarten. How many students are in kindergarten if the school has 50 students?

Answers

Answer:

10 students in Kindergarten

Step-by-step explanation:

20% is equal to 1/5

1/5 x 50 = 10 or 50 ÷ 5 = 10

Answer:

10 ig

Step-by-step explanation:

cause

the net of a retangular prism is shown below. The surface area of each face is labeled. 12 square centimeters, 12 square centimeters, 18 square centimeters, 18 square centimeters, 24 square centimeters, and 24 square centimeters. which values represent the dimentions, in centimeters, of the retangular prism?



HELP QUICKLY PLEASE

Answers

Answer:

76

Step-by-step explanation:

Please need help with this one

Answers

y-y1=m(x-x1)
x1 and y1 are coordinates of first point
x and y are coordinates of second point
(7,7) x1=7, y1=7
(-9,-1) x= -9, y= -1
-1-7=m(-9-7)
-8=m(-16)
-8= -16m multiply by -1
8=16m
m=8/16
m=1/2

Answer:

y - 7 = 1/2(x - 7)

Step-by-step explanation:

Point slope form is y - y1 = m (x - x1)

So find m = y2 - y1/ x2 - x1, so m = -1 - 7 / -9 - 7, m = -8 / -16 so m = 1/2

Then sub your (7,7) so y - 7 = 1/2(x - 7)

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 100 miles per hour. The westbound train
travels at 90 miles per hour. How long will it take for the two trains to be 304 miles apart? ( this is timed plz someone help)

Answers

Solving for the elapsed time

distance traveled = (speed of first train + speed of second train) * elapsed time

280 miles = (95 mph + 105 mph) * elapsed time

280 miles = 200 mph * elapsed time

elapsed time = 280 miles / 200 mph

elapsed time = 1.4 hours

elapsed time = 1 hour and 24 minutes

It will take 1 hour and 24 minutes for the two trains to be 280 miles apart.

Quadrilateral RUST has a vertex at R(2,3). What are the coordinates of R' after dilation by a scale factor of 3, centered at the origin, followed by the translation (x,y)->(x,y - 1)?

Answers

concept of this answer is (3,5) in the y(x)=-3

Answer: it’s (6,8)

Step-by-step explanation: I took the test

PLEASEEEEE I NEED HELPPPPP !!!!!!!

Answers

(Volume for a rectangular shape is length x width x height)

We can split up this 3D composite figure into two main parts (as shown in the picture I attached), and find each part’s volume before adding them together for the total volume.

Cube —> 5x5x5 —> 25x5 = 125 in^3

Rectangular Prism —> 20x5x5 —> 100x5 = 500 in^3

125 + 500 = 625

So the answer is A. 625 in^3

Hope this helped! If I was correct, I’d appreciate it if you marked my answer as Brainliest.

Graph f(x) = 3[x] +9

Answers

Answer:

Step-by-step explanation:

The equation of line is y = 3x + 9 , where the slope is m = 3

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = 3x + 9   be equation (1)

The equation is of the form y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

Slope m = 3

The y intercept of the line is ( 0 , 9 )

Now , the equation of line is plotted on the graph below

Hence , the equation of line is y = 3x + 9

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ5

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypotenuse into line segments of length x and y. Solve for h,x, and y.

Answers

Answer:

[tex]h = 12[/tex]

[tex]x = 9[/tex]

[tex]y= 16[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

[tex]A = \frac{1}{2} * 15 * 20[/tex]

[tex]i.e\ height = 20[/tex]

[tex]A = \frac{1}{2} * 300[/tex]

[tex]A = 150[/tex]

Let the base of the triangle be 25.

So, the area is:

[tex]A = \frac{1}{2} * 25 * h[/tex]

[tex]i.e\ height = h[/tex]

[tex]A = \frac{1}{2} * 25h[/tex]

Substitute [tex]A = 150[/tex]

[tex]\frac{1}{2}*25h = 150[/tex]

Solve for h

[tex]h = \frac{150 *2}{25}[/tex]

[tex]h = 6 *2[/tex]

[tex]h = 12[/tex]

Considering the smallest triangle

[tex]Hypotenuse = 15[/tex]

So:

[tex]15^2 = h^2 + x^2[/tex]

[tex]15^2 = 12^2 + x^2[/tex]

This gives:

[tex]15^2 - 12^2 = x^2[/tex]

[tex]81 = x^2[/tex]

Take square roots

[tex]9 =x[/tex]

[tex]x = 9[/tex]

Solving for y

[tex]x + y = 25[/tex]

[tex]y= 25 - x[/tex]

[tex]y= 25 - 9[/tex]

[tex]y= 16[/tex]

I need to figure out how many solutions does the system of equations below have.
y=6/7x-8 and y=7/9x+10/9

Answers

Answer:

The system has one solution.

Step-by-step explanation:

To find the number of solutions of the system, we equal both equations for y.

If we have ax = b, in which both a and b are different of 0, we have one solution.

If both a and b are 0, we have infinite solutions.

If a is 0 and b is not, there are no solutions.

y=6/7x-8 and y=7/9x+10/9

So

[tex]\frac{6x}{7} - 8 = \frac{7x}{9} + \frac{10}{9}[/tex]

[tex]\frac{6x}{7} - \frac{7x}{9} = \frac{10}{9} + 8[/tex]

[tex]\frac{54x - 49x}{63} = \frac{10}{9} + \frac{72}{9}[/tex]

[tex]\frac{5x}{63} = \frac{82}{9}[/tex]

[tex]45x = 63*82[/tex]

Both a and b are different of 0, so the system has one solution.

I need help ASAP will mark the brainliest

Answers

Answer: 7,3

Step-by-step explanation: do the x line the y line (not the best explanation)

Answer:

16,7

Step-by-step explanation:

The answer is 16,7 because y value will go up 3 since the JKLM is the same and x value will go right 10.

Y+3, x+10

Hope this help!

Can someone please help me it’s very important please ASAP

Answers

The answer to this question is c)

can someone pls help me w this

Answers

Answer:

a = 2

b = 1

c = 1

Step-by-step explanation:

The quadratic equation, 2x² + x + 1 = 0, is expressed in the standard form as ax² + bx + c, where a ≠ 0.

Thus,

a = 2

b = 1 (1 * x = x)

c = 1

Triangle ABC was transformed to create triangle A′B′C′.Which rule best describes this transformation?

Answers

Answer:

Option A is the answer buddy

Step-by-step explanation:

Answer:

a is the answer boi

Step-by-step explanation:

Hard question need help My mom is mad please help Middle school will like and give brainliest

Answers

Isiah, you have been to careless to cut out your tabs on your computer. Now a stranger knows you go to Belmont Ridge Middle School in Loudon Virginia.
Please learn about internet safety with an adult because stuff like this can be dangerous

Please answer ASAP this is due tomorrow

Answers

I found this answer online for the same question so i suppose this is it

Complete the solution of the equation. Find the
value of y when x equals 13.
-3x - 2y = -25

Answers

Answer:

y = -7

Step-by-step explanation:

I wrote how I did

and the steps

Answer: -7

Step-by-step explanation:

what is meaning of pictogram​

Answers

here u go

i hope u got it

A pyramid has a rectangular base that is 5 cm wide and 9 cm long. The height of the pyramid is 10 cm.
10 cm
5 cm
9 cm
What is the volume of the pyramid?

Answers

Answer:  450 cm

Step-by-step explanation:

10 x 9 = 90 x 5 = 450

someone help me ASAP

Answers

Answer:

there's nothing here at all....

Step-by-step explanation:

So I need help on this

Answers

i cant really see it but i think petrified fossil
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