An IQ test is designed so that the mean is 100 and the standard deviation is 21 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with ​99% confidence that the sample mean is within 6 IQ points of the true mean. Assume that σ=21 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answers

Answer 1

Answer:

The required sample size is 82. This number of people could be sampled in an afternoon, for example, at a commercial center in a city, which means that it is a reasonable sample size for a real world calculation.

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.

Assume that σ=21 and determine the required sample size.

A sample size of n is needed.

n is found when M = 6. So

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

[tex]6 = 2.575\frac{21}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 2.575*21[/tex]

Dividing both sides by 3

[tex]\sqrt{n}= 2.575*3.5[/tex]

[tex](\sqrt{n})^2 = (2.575*3.5)^2[/tex]

[tex]n = 81.2[/tex]

Rounding up:

The required sample size is 82. This number of people could be sampled in an afternoon, for example, at a commercial center in a city, which means that it is a reasonable sample size for a real world calculation.


Related Questions

5
Which of the following is the result of expanding 22"-2,
n=1
O 8.5
O 15.5
O 32
60

Answers

Answer:

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 15.5[/tex]

Step-by-step explanation:

Given

[tex]\sum\limits^5_{n=1} {2^{n-2}[/tex]

Required

The result

To do this, we simply substitute 1 to 5 for n.

So, we have:

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 2^{1-2} + 2^{2-2} + 2^{3-2} + 2^{4-2} + 2^{5-2}[/tex]

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 2^{-1} + 2^{0} + 2^{1} + 2^{2} + 2^{3}[/tex]

Evaluate each exponent

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 0.5 + 1 + 2 + 4 +8[/tex]

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 15.5[/tex]

Answer:

Answer is B edg2021

soknasoiegspeoigapoiegaoig

Watch help vile
Write an explicit formula for an, the nth term of the sequence 19, 25, 31, .....

Answers

19,25,31,37,43,49,55,61, 67
67 is the ninth term!!

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7.5 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 30.5 grams per pound. Find the probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

Answers

Answer:

0.121 = 12.1% probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7.5 grams of fat per pound.

This means that [tex]\mu = 32, \sigma = 7.5[/tex]

Sample of 34:

This means that [tex]n = 34, s = \frac{7.5}{\sqrt{34}} = 1.2862[/tex]

Find the probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

This is the pvalue of Z when X = 30.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{30.5 - 32}{1.2862}[/tex]

[tex]Z = -1.17[/tex]

[tex]Z = -1.17[/tex] has a pvalue of 0.121

0.121 = 12.1% probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

is 1 5/6 a rational number or a iraarational

Answers

Answer: rational number

Step-by-step explanation:

Mixed numbers are all rational numbers because they can be expressed as a fraction. To be a rational number, a number must be able to be written

What are the maximum, minimum, range and mean?

Answers

Yh maximum is 6 and the minimum is 1

Amanda runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?

Answers

Answer:

5.6 miles

Step-by-step explanation:

[tex]\frac{7}{80} =\frac{x}{64}[/tex]   Set up the proportion

[tex]7(64)=x(80)[/tex]  Cross multiply

[tex]448=80x[/tex]     Simplify

[tex]\frac{448}{80}=\frac{80x}{80}[/tex]    Divide both sides by 80

[tex]5.6=x[/tex]

The diameter of a pizza is 45 inches. What is the area of where we would be able to put all ingredients
on top of the pizza?

Answers

Answer:

the area of the pizza is 1590.43 in. :)

Step-by-step explanation:

Identify whether the following equation has a unique solution, no solution, or infinitely many solutions. 3 + 5= 8

Answers

Answer:

to me it's a simple solution

Step-by-step explanation:

Answer please and explain

Answers

Answer:

C=84

Step-by-step explanation:

Since you use 3 for pi. You plug the radius into the formula. C=2×3x14=84

In the picture, the radius is 14, this stands for r in the equation givin. Also pie is equivalent to 3. You then plug in the numbers into the equation. You can see this in the work I gave. You then times all of the numbers together it get your final answer or 84

Help please 20 points for anyone

Answers

Answer:

The answer is B!

Step-by-step explanation:

I hope this helps! Have a great rest of your day!

Will give brainliest for correct answer

Answers

Answer:

The first picture on the second page

Step-by-step explanation:

The first picture on the second page would be the answer because it gives exactly one input for each output. It also passes the vertical line test because no point throughout the line creates a vertical line.

The first picture, none of the x values have 2 answers.

Line t is tangent to the circle . Find AB (click photo)

Answers

Answer:

mAB=130°

Step-by-step explanation:

The tangent-chord theorem tells us that the angle the tangent makes with the curve (65°) is half the measure of the arc (mAB):

mAB=2(65)=130°

The value of measure of arc AB is,

⇒ m AB = 130°

           

What is mean by Angle?

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Line t is tangent to the circle.

Now, We know that;

The tangent-chord theorem tells us that the angle the tangent makes with the curve is half the measure of the arc.

Hence, We can formulate;

⇒ m AB = 2 × 65°

              = 130°

Thus, The value of measure of arc AB is,

⇒ m AB = 130°

           

Learn more about the angle visit:;

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offering 19 points to whoever can solve this need the answers

Answers

Answer:

Excuse Me! I believe you forgot to add your question and or picture with the question(s) in it! I would highly recommend to re-upload your question(s) to get the desired information needed!

Yours Truely, TheAnimeCatUwU

Please help !!!! Please help!!!!! I gave extra points, if you put a link I will report you !

Answers

Answer:

7x+7+5x+14=13x+10

12x+21=13x+10

-12x       -12x

21=x+10

-10    -10

x=11

13(11)+10

angle 4=153

Step-by-step explanation:

I solved it by using my big brain.

is 2 a solution to 2x+3<2 ?

Answers

Answer:

no

Step-by-step explanation:

2(2) + 3 < 2  is a False statement; therefore, 2 is not a solution

Lucas used the number sentence 8 x 2 = 16 to solve a problem. Which problem could he have solved? ​

Answers

Answer:

Word problem 3        

Step-by-step explanation:

Word Problem one is a subtraction problem since Felicia is giving away two marbles to Lucas. Word Problem two is a division problem since Felicia is evenly dividing the number of marbles she has into two bags. Word Problem three is a multiplication problem because Ryan has two times as many marbles that Felicia does. Word Problem four is an addition problem because she found two more marbles while she already has eight marbles. Keywords for subtraction word problems are: fewer than, decrease, take away, less than, minus, difference, change, lost reduced, and subtract. Keywords for division word problems are: As much, cut up, groups, equally, sharing, half, how many in each, parts, per percent, quotient, ratio, and separated. Keywords for multiplication word problems are: double, every, factor, increased, multiplied product, times, and tripled.

An Oil Rig is 30 meters tall. Mr. Clanton is standing 12 meters from the base of the Rig. At what angle of elevation does he need to look to see the eagle on top of the Rig ? What is the distance from Mr. Clanton to the Eagle ?

Answers

Answer:

Angle of elevation: 68.2°, distance from Mr. clanton to the eagle: 32.3m.

Step-by-step explanation:

I can't draw the diagram , but will try to explain:

the diagram is a right angled triangle, with the opposite as the rig, the adjacent as the distance between mr. clinton and the base of the rig, and the hypotenuse as x.

∅ is the angle of elevation from clinton to the eagle.

Using SOH CAH TOA,

Tan∅ =30÷12

tan∅ =2.5.

∅ =tan^-1( tan raised to power -1 )

∅ =tan^-1(2.5)

∅ = 68.19859051≅68.2 to 3s.f.

To get the distance between mr. clinton and the eagle:

Using SOH CAH TOA;

Cos68.2 =12/x   cross multiplying....

x*cos68.2 =12

∴ x = 12 ÷ cos 68.2

= 12 ÷ 0.3713678356

= 32.31297611≅32.3 to 3s.f.

Hope this helps.....

4 tran ra To make cherry trail mix, Sebastián needs 4 oz of nuts for every 3 oz of dried cherries. To make sunflower trail mix, he needs 5 oz of nuts for every 2 oz of sunflower seeds. Can Sebastián make more cherry trail mix or sunflower trail m with 20 oz of nuts? Show your work. OLUTION metale to make bronz bronz​

Answers

For starters I am not 100% sure of if this is correct I may not understand the quest so bare with me

Answer:

Cherry Trail Mix

Step-by-step explanation:

4 oz of nuts for every 3 oz of dried cherries

5 oz of nuts for every 2 oz of sunflower seeds

- Multpy the amount of nuts in each bag to 20 - Cherry Trail Mix: 4*5=20

Sunflower Trail Mix: 5*4=20

- Now multiply the amount of dried cherries and sunflower seeds by the number used to get to 20

Cherry Trail Mix: 3*5= 15 Sunflower Trail Mix: 2*4=8

- Now add up the amount of oz in each

Cherry: 20+15=35

Sunflower: 20+8=28

35oz > 28oz

HELP HELP HELP

A zoologist studied the wild cat population of two islands during a four year span - Meow Island and Purr Island. She collected the following data about the population.



1. How would you describe the growth of each island ?

2. Which do you think will be modeled by a linear function ?

Answers

Answer:

Meow Island has a linear function.

Step-by-step explanation:

Meow Island increases by multiply the input by 3 for each coordinate. On the other hand, Purr Island increases by adding 4. Linear functions increase with multiplication, not by addition, and so Meow Island increases linearly.

Decrease £140 by 22%

Answers

Answer:

109.2

Step-by-step explanation:

math

Part A: Write an algebraic expression for 8 more than 5 times a number. (5 points)

Part B: Write a verbal expression for 4(n + 6). (5 points)

Answers

Part A: 5x + 8

Part B: The sum of 6 and a number, increased 4 times.

The algebraic expression for [tex]8[/tex] more than [tex]5[/tex] times a number will be [tex](8+5x)[/tex] and the verbal expression for [tex]4(n + 6)[/tex] will be four times the sum of a number and six.

What is expression ?

Expressions is a finite combination of symbols that is well-formed according to rules that depend on the context.

Part A ;

We have,

[tex]8[/tex] more than [tex]5[/tex] times a number

Now,

Let a number [tex]=x[/tex]

So,

According to the question,

We get, [tex](8+5x)[/tex]

So, this is the algebraic expression .

Part B ;

We have,

[tex]4(n + 6)[/tex]

So,

According to the question,

[tex]4(n + 6)[/tex] will be written as four times the sum of a number and six.

So, this is the verbal expression .

Hence, we can say that the algebraic expression for [tex]8[/tex] more than [tex]5[/tex] times a number will be [tex](8+5x)[/tex] and the verbal expression for [tex]4(n + 6)[/tex] will be four times the sum of a number and six.

To know more about expression click here

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Paying my bills late will most likely cause my credit score to go down.

True or False

(GIVING BRAINLIEST)

Answers

Answer:

True

Step-by-step explanation:

For each set of measures, choose whether the conditions determine a unique triangle, more than one triangle, or no triangle.

Answers

Answer: 1st unique 2nd nothing 3rd more than 1

Step-by-step explanation:

giving 10 brainlist to whoever gets it RIGHT​

Answers

0.001276 is the correct answer!10 x 10 x 10 x 10 x 10 = 100,000127.6 ÷ 100,000 = 0.001276Please let me know if I am wrong.

Answer:

.001276

Step-by-step explanation:

127.6 ÷ 10^5

Dividing by 10^5 means we are moving the decimal 5 places to the left

We need to add zeros in front of the number to move it to the left

00127.6

Now move it 5 places

.001276

The predicted population of Andover t years after 2010 can be modeled by the following equation.
g(t) = 900(1.02)
The predicted population of Hornell t years after 2010 can be modeled by the following table.
t 0 5 10 15 20
f(t) 1,000 1,762 3,105 5,473 9,646
Based on these predictions, which city will have a greater average rate of change in population between 2010 and 2020?
O Both cities will have the same average rate of change of population.
O This cannot be determined from the given information.
O Andover
O Hornell

Answers

Answer:

Step-by-step explanation:

Answer: Hornell

Step-by-step explanation:

Please Help!!!!!!
I need the answer ASAP!

Answers

Bro use Socratic that will help you.

Question is down in the image

Answers

Answer:

It is (33.3) [Last one]

Step-by-step explanation:

I hope that is useful for you :)

This equation is basically 35.6 -2.3, you just reverse the numbers

35.6

-  2.3

33.3

The answer is D

A football stadium contain 80% of its full capacity of spectators for a grand final match. At the end of the game, spectators leave the ground through various exits at the rate of 5 spectators per seconds. After 20 minutes the stadium contain 60% of its full capacity of spectators.
A. Calculate the full capacity of the stadium
B. How many spectators will be in the stadium 1 hour after the end of the game?

Answers

Answer:

A. 30000

B. 12000

Step-by-step explanation:

Find out how much spectators leave in 1 minute.

1 second = 5

1 minute = 5 x 60 = 300 (60 seconds)

20 minutes = 300 x 20 = 6000

Since there were only 80% of the full capacity of spectators and after minutes it became 60%...

80% - 60% = 20%

20% = 6000

1% = 6000 ÷ 20 = 300

100% = 300 x 100 = 30000

1 minute = 300 spectators leaving

1 hour = 300 x 60 = 18000 (60 minutes)

30000 - 18000 = 12000

Question 8: 10 pts
Find the magnitude and direction of the vector <3,9>. Round angles to the nearest degree and other values to
the nearest tenth.

Answers

Answer:

9.5; 72˚

Step-by-step explanation:

When building a house, the number of days required to build is inversely proportional
to with the number of workers. One house was built in 132 days by 4 workers. How
many days would it take to build a similar house with 16 workers?

Answers

Answer: 33

Step-by-step explanation:

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