The weights of gala apples follow a Normal distribution with a mean of 140 grams and a standard deviation of 12 grams. The owner of an apple orchard randomly selects 5 apples from the harvest and records the mean weight. What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

Answers

Answer 1

Answer:

The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.

Step-by-step explanation:

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.

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]

What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

By the Central Limit Theorem, the shape is approximately normal.

Mean is [tex]\mu = 140[/tex]

Standard deviation is [tex]s = \frac{12}{\sqrt{5}} = 5.37[/tex]

The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.


Related Questions

What is the volume of the pyramid in the diagram?
25 cm
h = 15 cm
15 cm
20 cm
OA 1,500 cm
OB. 2,500 cm
OC 4.500 cm

Answers

Answer:

Step-by-step explanation:

Wheres the diagram??

Incomplete q

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost ​$81.23 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost ​$77.17. How much does an average movie ticket cost in each of these​ countries?

Answers

Answer:

Let the cost in Japan be m and that of Switzerland be n

n=13.35

Step-by-step explanation:

Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

(6x + 5)(x2 – 2)
(6x – 5)(x2 + 2)
(6x2 + 5)(x2 – 2)
(6x2 – 5)(x2 + 2)

Answers

Answer:

(6x2 - 5)(x2 + 2)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Which equation has a greater rate of change than the rate shown in the
table below?
х
0
2
4
6
8
у
5
5.5
6
6.5
7

Answers

pretty sure it’s option 1

What part of a hummingbird is adapted to help it obtain food from inside flowers?
1.Beak
2.Wings
3.Eyes
4.Head

Answers

1 Beak. I hope this helps

The value of Adam's model railway is $550.
This value increases exponentially at a rate of r %
per year.
At the end of 5 years the value will be $736.
Calculate the value of r.

Answers

Answer:(c)

Step-by-step explanation:

Given

The initial value of Adam's model is [tex]A_o=\$550[/tex]

the value increases exponentially with the rate of [tex]r\%[/tex]

Time period [tex]t=5\ years[/tex]

Final amount [tex]A=\$736[/tex]

Exponential growth is given by

[tex]\Rightarrow A=A_o(1+r)^t[/tex]

Putting values

[tex]\Rightarrow 736=550(1+r)^5\\\\\Rightarrow (1+r)^5=1.338[/tex]

[tex]\Rightarrow 1+r=1.05999\\\Rightarrow r=0.05999\ or\ 5.99\%\approx 6\%[/tex]

Option (c) is correct

mike made 5 fewer than three times the number of bracelets that sheri made. Write an expression to represent the number of brackets mike made. then determine the number of bracelets that mike made if sheri made 12 bracelets

Answers

Answer:

the answers are in the pic

Step-by-step explanation:

i needa big mac frfr brrrrrrrr

Answers

Answer:

ok

Step-by-step explanation:

Answer:

suppersize my fries...

What is the relative minimum of the function?
if anyone could help it would be appreciated!! :)

Answers

Answer:

-2

Step-by-step explanation:

since the parabola opens upwards, the minimum is at the vertex of the parabola and the maximum is infinity, because the lines of a parabola goes on forever

you look for the smallest x value for the parabola and since you can see that the vertex of the parabola lies on x=-2, the minimum value of the function is -2.

Hope that helps :)

Which of the following is equivalent to the complex number i²22

Answers

Answer:

yes I am pretty sure that's correct

HELP ASAP!!!!!! PLEASE

Answers

Answer:

(x,y) --> (-y,-x) is the rule

Step-by-step explanation:

(-1,3) to (-3,1)

Hope I helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Which problem is even below
4,323
944
291
31

Answers

944 let me know if that’s right

HOW DO YOU DO THIS PLEASE EXPLAIN

Answers

Answer:

70 degrees

Step-by-step explanation:

it’s a bit hard to explain

On a scale drawing of a building, 1 inch represents 14 feet. If the height of the actual building is 49 feet, what is the height of the drawing?

enter the answer in the text box below

____ in.

Answers

The answer is 3.5 inches for K12 test

All i did was see what coud make 49 feet.

since 1 inch = 14 feet then i did 3 x 14 which got 42.

I then just shuffled around numbers and got 3.5.

THE ANSWER IS 3.5

Very sorry if its wrong

I need help I can’t cuaet understand this

Answers

Answer:

B, 140

Step-by-step explanation:

Alright so if you know to do volume this should be a breeze!

First off what you want to do is find the volume of the outside prism.

V=whl=4·5·8=160

160

Then find the smaller prisms volume.

V=whl=1·5·4=20

20

Minus the smaller from the bigger

160-20=140

The answers B!

what is the slope of the line that passes through the points (2,-3) and (2,13)? write your answer in simplest form

Answers

Answer:

The slope is undefined because there is no change in x, making it a vertical line

Step-by-step explanation:

Please help test due in 1 hour and it’s a grade! Will give brainliest and good review!

Answers

Answer

The measurement of the missing sides are 4 cm on each side

Step-by-step explanation:

multiply 5 times 2 (5x2=10) take away the 10 and 18 and the answer for it is the answer for the whole thing.

What is 5 3/4 - 6 1/2

Answers

Answer:

-1 1/4

Step-by-step explanation:

1/2 - 2/4

5 - 6 = -1

3/4 - 2/4 = 1/4

-1 1/4

Hope this helped! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

2p(7p+7) please answer

Answers

Answer:

14[tex]p^{2}[/tex] + 14p

Step-by-step explanation:

to expand, multiply 2p with 7p which gives you 14p^2

then,

multiply 2p by 7 = 14p

14p to the 2nd power+14p

Find the values of X,Y and z

Answers

Answer:

x = 11.31

y = 13.86

z = 19.60

Step-by-step explanation:

8/x = x/16

x^2 = 128

x = 11.31

x^2 + 8^2 = y^2

128 + 64 = y^2 = 192

y = 13.86

x^2 + 16^2 = z^2

128 + 256 = z^2

z^2 = 384

z = 19.60

Box A contains 3 red and 2 blue marbles while Box B contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box A; if it turns up tails, a marble is chosen from Box B.
A. Find the probability that a red marble is chosen.
B. Referring to above information, suppose that the person who tosses the coin does not reveal whether it has turned up heads or tails (so that the box from which a marble was chosen is not revealed) but does reveal that a red marble was chosen. What is the probability that Box A was chosen (i.e., the coin turned up heads)?

Answers

Answer:

A. [tex]\frac{4}{10}[/tex]

B. [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given - Box A contains 3 red and 2 blue marbles while Box B contains 2

            red and 8 blue marbles. A fair coin is tossed. If the coin turns up

            heads, a marble is chosen from Box A; if it turns up tails, a marble

            is chosen from Box B.

To find -  A. Find the probability that a red marble is chosen.

              B. Referring to above information, suppose that the person who

                  tosses the coin does not reveal whether it has turned up

                  heads or tails (so that the box from which a marble was

                  chosen is not revealed) but does reveal that a red marble was

                  chosen. What is the probability that Box A was chosen (i.e.,

                  the coin turned up heads)?

Proof -

As given ,

Box A : 3 red marbles and 2 blue marbles.

Box B : 2 red marbles and 8 blue marbles.

a.)

As we have to find the probability that a red marble is chosen.

A red marble is chosen in two different ways - either it can be from Box A or Box be .

If Box A is chosen , then Probability of red ball is [tex]\frac{3}{5}[/tex]

If Box B is chosen , Then Probability of Red ball is [tex]\frac{2}{10} = \frac{1}{5}[/tex]

Now,

Probability of Box A is Chosen = [tex]\frac{1}{2}[/tex]

Probability of Box B is chosen = [tex]\frac{1}{2}[/tex]

∴ we get

Probability that a Red marble is chosen =  [tex]\frac{1}{2}[/tex]×[tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex]×[tex]\frac{1}{5}[/tex] = [tex]\frac{3}{10} + \frac{1}{10} = \frac{4}{10}[/tex] = 0.4

b.)

Now,

Probability that Box A is chosen given that Red marble is chosen is

P(Box A | Red marble ) = [tex]\frac{(\frac{3}{5})(\frac{1}{2}) }{(\frac{3}{5})(\frac{1}{2}) + (\frac{1}{5})(\frac{1}{2})} = \frac{\frac{3}{10} }{\frac{3}{10} + \frac{1}{10} } = \frac{\frac{3}{10} }{\frac{4}{10}}[/tex] = [tex]\frac{3}{4}[/tex]

What is the area of the triangle?
8
4

Answers

area of triangle is base x height divide by 2
8x4=32
32 divide by 2 is
16

Look at the picture.
Thank u!

Answers

Answer:

I'm pretty sure its 16/30 = 8/15

Step-by-step explanation:

I don't know what simplify expressions means, I do know how to convert decimals into fractions and multiply fractions so.

Can someone help with this asap ?

Answers

Answer:

y=-(x+11)(x-23)

Step-by-step explanation:

y=-(x+11)(x-23)

use the x intercepts they give you, and make it the opposite i.e. if it positive, then make it negative if it is negative make it positive

i.e. -11 equals 11

thus (x+11)

then, the graph is concave down, so it is negative at the front

Determine the amount or number of something mathematically

Answers

2.586 is the answer cause you said mathematically

Geometry proof help please

Answers

Answer:

the picture is blurt can't see any thing sorry can't help

pls pls pls pls helpppp it's 12:10am

Answers

Answer:

I guess it will be (D) 4/3=$4.41/x

An employee's salary,
S
(
n
)
, in dollars, at a company is a function of the number of years,
n
, that the employee has worked at the company.

The relationship between
n
and
S
(
n
)
is shown in the table below.

Answers

The question is incomplete. Here is the complete question.

An employee's salary, S(n), in dollars, at a company is a function of the number of years, n, that the employee has worked at the company.

The relationship between n and S(n) is shown in the table below.

Which of the following equations represents an explicit formula for S(n)?

A. S(n) = 40,000(1.05)ⁿ

B. S(n) = 40,000 + 1.05n

C. S(n) = 40,000(1.05)ⁿ⁻¹

D. S(n) = 40,000 + 1.05(n-1)

Answer: A. S(n) = 40,000(1.05)ⁿ

Step-by-step explanation: The table shows an exponential function, which is, in general, is of the form:

[tex]S(n)=S_{0}r^{n}[/tex]

where

S₀ is the initial value

r is the rate the salary grows

n is the years the employee worked

From the table, in the first year, an employee receives $40,000, so, that is the initial value.

The salary increases at a constant rate of 1.05 per year, as shown below:

[tex]r=\frac{42,000}{40,000}=\frac{44,100}{42,000}=\frac{46,305}{44,100}[/tex]

r = 1.05

So, the rate the salary grows is r = 1.05 or 5%.

Therefore, the equation that shows an explicit formula for S(n) is [tex]S(n)=40,000(1.05)^{n}[/tex].

Nayla delivers 63 magazines on Saturday and 72 magazines on Sunday. She makes bundles of 9 magazines for each of her delivery routes. How many delivery routes does Nayla have on Saturday and​ Sunday?

Answers

Answer:

14

Step-by-step explanation:

9*6=63

9*8=72

6+8=14

5,890,000=a×10b a==?

Answers

Answer:

=146628

Step-by-step explanation:

gracias por los puntos

Other Questions
Round 38224 correct to 1 significant figure Explain why the same side of the moon is always facing Earth. Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of shirts would the cost be the same? What are the variables, equations, and how do you solve? Which of the following does NOT describe a way in which alcohol influences sexualactivity?lowers inhibitions promotes safe behaviorscompromises moral standards Suppose a motorcycle costs $8,000 and loses 4% of its value each year. What will be the value of the motorcycle after 7 years? How did the British colonies in North America (the futureUnited States) differ from the Spanish and Portuguese colonies of Latin America? please help and thank you If point (7.b) is in Quadrant I and point (a.--3)is in Quadrant III, in which Quadrant is the point(a,b)? 3. Vivian has a balance of $1,075 in a savings account that pays 3.25% interest compounded annually. If Vivian makes no deposits or withdrawals, how much money will be in her saving account after 24 months? Mhanifa please help I will mark brainliest! Calcium carbonate decomposes to form calcium oxide and carbon dioxide, like this:CaCO3(s)CaO(s)+CO2(g)At a certain temperature, a chemist finds that a 9.0L reaction vessel containing a mixture of calcium carbonate, calcium oxide, and carbon dioxide at equilibrium has the following composition:Compound AmountCaCO3 25.3 gCaO 14.9 gCO2 33.7 gCalculate the value of the equilibrium constant Kc for this reaction. Round your answer to 2 significant digits. Some students conduct an investigation in a biology lab by setting up four different artificial stomachs, each in a40 C water bath. The students place the same amount of boiled egg white, a protein-rich source, in each stomach.They also add dilute hydrochloric acid, HCl, and pepsin, a digestive enzyme, to each stomach, as shown in the table.The students observe the mass of egg white in each stomach every 15 minutes.Which statement describes the most likely result of this investigation?A. The mass of the Egg white increases as the volume of the enzyme increases.B. The egg white is unaffected by the differing amount of enzyme.C. Digestion decreases in each stomach as more of the egg white's surface area becomes exposed.D. Digestion increases as the volume of the enzyme increases. What is 8/9ths of 4? Mexicans ur not gonna like what im about to say: TACOBELL.. is there anyone who can find the x and y intercepts of y = log 4 (x + 16) - 1? I could not find any subject that was close to forensics, so I chose a random one. PLEASE HELPA person who has never been arrested commits a crime. An eyewitness sees a person running from the crime scene. What method could investigators use to help locate the person? 1. Tax Law is a source ofLabour LawPublic Law"Procedural lawO International Law (-3,-4)&(-2,-8)find the slope between the two points A home has a room with length 22 feet and width 25 ft.Which dimensions could represent a scale model of the room?O length = 6.5 in.; width = 7.5 in.O length= 11 in.; width = 12.5 in.O length = 13 in.; width = 14 in.O length = 17.6 in.; width = 19.5 in. PLEASE HURRY Triangle RST has vertices R(6,2), S(2,8), and T(4,2).Determine the transformation of triangle RST that produces triangle RST.R(6,2), S(2,8), T(4,2)reflection across the x-axisreflection across the y-axisreflection across the line y = xrotation clockwise 90 about the origin