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.

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

Instructions: Find the missing side lengths. Leave your answers
radicals in simplest form.
Please help, no links

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?

Choose the item that has measurable volume.
a dollar bill
a page from a magazine
a quiz paper
a jug of milk

Plz help me well mark brainliest if you are correct!!....

Out of 195 students, 9% have
hazel eyes. How can you estimate the number of
students with hazel eyes?

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

Help me out !!!!!!!!!!

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

Question: What is 4 - 1/8

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)

Find the side length of
square area of 50 cm^2? find the perimeter.

Given:

VC, CU - secants

Prove: CI·CU = CJ·VC

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?

Please help! 25 points! Find the sum of the first 6 terms of the following series, to the nearest integer.

28, 112, 448,....

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.

Find the area of the polygon shown. Enter the number into the box.
ft? 1 ft 4 ft 4 ft

Someone please help me with this.

I don’t know how to solve this I’m so confused please help me

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

Find the missing side length please help!!!

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)

Can someone please help me please....

Find the value of x. Round to the nearest degree.

Not drawn to scale

Evaluate: 3 x 23 x 4² x 3-7x4-2​

I need the answer pls I really neeed it

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!)

Simplify: −(−(−78))
Write answer in numerical value

(8-5/2-2)-4
=?

Please helping me!!!

Plz help me well mark brainliest if correct!!...

Help thank yoy if you do. Please eat if you havent today remember i love you​