According to the 2000 U.S. Census, 80% of Americans over the age of 25 have earned a high school diploma. Suppose we take a random sample of 120 Americans and record the proportion, p, of individuals in our sample that have a high school diploma.
Answers
Answer:
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
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]
80% of Americans over the age of 25 have earned a high school diploma.
This means that [tex]p = 0.8[/tex]
Suppose we take a random sample of 120 Americans
This means that [tex]n = 120[/tex].
Question a:
The mean is:
[tex]\mu = p = 0.8[/tex]
The mean is 0.8.
Question b:
The standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.8*0.2}{120}} = 0.0365[/tex]
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Here, we have,
we know that,
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean x and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean x and standard deviation s = σ/√n .
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean x=p and standard deviation s=√p(1-p)/n
80% of Americans over the age of 25 have earned a high school diploma.
This means that p=0.8
Suppose we take a random sample of 120 Americans
This means that n=120.
Question a:
The mean is:
x=p=0.8
The mean is 0.8.
Question b:
The standard deviation is:
s=0.0365
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ6
Related Questions
Five hundred sixth-grade students
were surveyed. Of these students
that were surveyed...
• 375 had been to a baseball game
• 270 own either a cat or a dog
• 125 had traveled on an airplane
3) What is the ratio of total sixth-grade students to the number of students who either want a cat or a dog? (Write the ratio in THREE ways)
Answers
Answer:
The ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1
Solution:
Given that,
Five hundred sixth-grade students were surveyed
Which means,
sixth-grade students = 500
125 had traveled on an airplane
What is the ratio of total sixth-grade students to the number of students who had traveled on an airplane?
Therefore,
total sixth-grade students : students traveled on airplane = 500 : 125
Ratio = 500 : 125
Reduce to lowest terms,
Divide both sides by 5
Ratio = 100 : 25
Further reduce to simplest terms,
Divide both sides by 25
Ratio = 4 : 1
Thus the ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1
Step-by-step explanation:
Of the population of all fruit flies we wish to give a 90% confidence interval for the fraction which possess a gene which gives immunity to fungal infections. To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene. Give the margin of error for the 90% confidence interval. Round your answer to 3 decimal places.
Answers
Answer:
The margin of error for the 90% confidence interval is of 0.038.
Step-by-step explanation:
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]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene.
This means that [tex]n = 400, \pi = \frac{280}{400} = 0.7[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.7*0.3}{400}}[/tex]
[tex]M = 0.038[/tex]
The margin of error for the 90% confidence interval is of 0.038.
Plz help me well mark brainliest if you are correct!!....
Answers
Answer:
9
Step-by-step explanation:
the two lines on either sign of each number indicate absolute value, which is the numbers value from 0 (on a number line). You turn -12 and -3 into 12 and 3 and subtract as normal.
The absolute value of -12 is 12 and the absolute value of -3 is 3. So, |-12| - |-3| = 12 - 3 = 9
Jason ran 2.8 miles yesterday and 3.4 miles today making his two day average 3.1 miles. How many kilometers does he average? Round your answer to the nearest hundredth.
a. 4.991 km
b. 4.99 km
c. 9.98 km
d. 4.51
Answers
It’s C, 9.98 km
Please help! 25 points! Find the sum of the first 6 terms of the following series, to the nearest integer.
28, 112, 448,....
Answers
Answer:
595
Step-by-step explanation:
First term:
7
7 ⋅ 4 = 28
Second term:
28
28 ⋅ 4 = 112
Third term:
112
112 ⋅ 4 = 448
Fourth term:
448
This geometric sequence can be further described by the equation:
aₙ = 7 ⋅ 4 ⁿ⁻¹
So if you want to find the 4th term, n = 4
a ₄ = 7 ⋅ 4 ⁴⁻¹ = 7 ⋅ 4 ³ = 7 ⋅ 64 = 448
Note:
aₙ = a₁ rⁿ ⁻¹
Help thank yoy if you do. Please eat if you havent today remember i love you
Answers
Find the area of the polygon shown. Enter the number into the box.
ft? 1 ft 4 ft 4 ft
Answers
Answer:
The area of the trapezium is 18 ft²
Step-by-step explanation:
Given;
Two parallel sides of the polygon as follows;
The first parallel side = 1 ft + 4 ft = 5 ft
The second parallel side = 4 ft
If this polygon is rotated 90 degrees, it forms a trapezium with a height of 4 ft.
The area of a trapezium is calculated as;
[tex]A rea= \frac{1}{2} (sum \ of \ parallel \ sides) \times height\\\\Area = \frac{1}{2} (5 \ + \ 4) \times 4\\\\Area = 18 \ ft^2[/tex]
Therefore, the area of the trapezium is 18 ft²
Find the side length of
square area of 50 cm^2? find the perimeter.
Answers
Answer:
100cm
Step-by-step explanation:
Because 50x2=100 cm
Can someone please help me please....
Answers
Answer:
a
Step-by-step explanation:
len
2. Demetri wakes up at 9:15. It takes him
35 minutes to fold 4 loads of laundry,
35 minutes to bathe the dog, 45 minutes
to bake brownies, and 1 hour to mow the
lawn. After he finishes all of his chores,
he sits down to rest. What time does
Demetri rest?
Answers
Answer:
I think the answer is 11.20 am
Choose the item that has measurable volume.
a dollar bill
a page from a magazine
a quiz paper
a jug of milk
Answers
Answer:
A jug of milk
Step-by-step explanation:
Someone please help me with this.
Answers
Answer:
fjf brotherhood handy urgency if it's by Griffith Jr it cuz if he by us if he my na na na hg hg hhbnnnnnñmmmmnnnnnnnn
Justin has a 2pound bag of Lima beans that he want to divide between 3families.how many pound of Lima beans should each family's receives? A. 3/2 pound b.2/3 c.2 1/3 pound d.3 1/3 pounds
Answers
Answer:
2/3 lbs
Step-by-step explanation:
2 divided by 3=2/3=2/3
Happy learning!
(8-5/2-2)-4
=?
Please helping me!!!
Answers
Answer: Hope This Helps!
Step-by-step explanation:
Simplify the expression.
Exact Form:
87/40
Decimal Form:
2.175
Mixed Number Form:
2 7/40
The slope of the line below is 0.4. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(-5, -3)
Answers
y + 3= 0.4(x + 5)
Jamie's Famous Hamburgers has 423.1 pounds of hamburger. If Jamie sells 279.51 pounds of hamburger for lunch now, how many pounds will be left over for dinner? (Try to do this problem without a calculator!)
Answers
Answer: The answer is 143.59
Step-by-step explanation:
I just subtracted 279.51 from 423.1! :)
Curts kite is 36 yards above the ground and directly above the tree. The length of the string from Curt to the kite is 49 yards. How far is Curt from the tree?
Answers
Answer:
about 33.24 yards
Step-by-step explanation:
a² + b² = c²
so, 36² + b² = 49²
1296 + b² = 2401
b² = 1105
Take the square root of both sides..
b = 33.24 yards
Which system of linear equations has exactly one solution?
2y = 10x + 4
y = 5x - 2
y = 2x - 3
2y = x - 12
y = 8x + 3
y = 8x + 7
15y = 30x + 90
y = 2x + 6
Answers
Answer:
y = 2x - 3
2y = x - 12
Step-by-step explanation:
Instructions: Find the missing side lengths. Leave your answers
radicals in simplest form.
Please help, no links
Answers
Answer:
Im pretty sure the first one is [tex]4\sqrt{3}[/tex]
and the second is 4
I need the answer pls I really neeed it
Answers
Help me out !!!!!!!!!!
Answers
Evaluate: 3 x 23 x 4² x 3-7x4-2
Answers
Simplify: −(−(−78))
Write answer in numerical value
Answers
Answer:
-78
Step-by-step explanation:
We need to find the value of -(-(-78))
We know that, -(-x) = +x
And -(-(-x)) = -x
We have,
x = 78
When two minus gets multiplied, we get a positive number and when a minus and a plus gets multiplied, we get a negative number. So,
-(-78) = +78
And
-(-(-78)) = -78
So, the numerical value is -78.
Plz help me well mark brainliest if correct!!...
Answers
Answer:
A/5
Step-by-step explanation:
There are 2 people after 5 in the the 4| part and 3 under 6 in the 5| part.
I don’t know how to solve this I’m so confused please help me
Answers
Answer:
240 inches squared
Step-by-step explanation:
12 x ( 3 + 17) =
12 x 20 =
240 inches squared
Out of 195 students, 9% have
hazel eyes. How can you estimate the number of
students with hazel eyes?
Answers
Answer:
round it to 18 since 9% of 195 is 17.55
Step-by-step explanation:
Question: What is 4 - 1/8
Answers
Answer:
The answer is 3 7/8 or 3.875
Find the missing side length please help!!!
Answers
Answer:
x = 15.9
Step-by-step explanation:
Recall: SOHCAHTOA
Reference angle = 25°
Opposite = x
Adjacent = 34
Apply the trigonometric function, TOA, since the Opp and Adj are involved
Thus:
Tan 25° = Opp/Adj
Tan 25° = x/34
34*Tan 25° = x
15.8544604 = x
x = 15.9 (nearest tenth)
Find the value of x. Round to the nearest degree.
Not drawn to scale
Answers
Answer:
Dude Where's the Diagram?
Given:
VC, CU - secants
Prove: CI·CU = CJ·VC
Answers
Answer:
this should help
Step-by-step explanation:
https://answer-helper.com/mathematics/question16732528
Answer:
No answer sorry