Answer:
Necesita cubrir 4800 cm^2.
Step-by-step explanation:
La pregunta está incompleta:
Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.
Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.
Para calcular el área simplemente multiplicamos las medidas de ambos lados:
[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? A: x^2 + 8x – 308 = 0 B: x^2 – 8x + 308 = 0 C: x^2 + 8x + 308 = 0 D: x^2 − 8x − 308 = 0
Answer:
A
Step-by-step explanation:
The smaller negative integer is x.
The larger one is x+8, since they are 8 units apart.
The equation would be:
x*(x+8)=308
Let's simplify it by distributing.
x^2+8x=308
Subtract 308 from both sides.
x^2+8x-308=0
Therefore, the answer would be A.
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
Learn more about the right angle triangle property here;
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Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
A cylindrical tank has a radius of 2 m and a height of 9 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)
Answer:
3,325,140 Joules
Step-by-step explanation:
Work done by the pump = Force applied to pump * distance covered by the water.
Since Force = mass * acceleration due to gravity
Force = (density of water * volume of the tank) * acceleration due to gravity
F =ρVg
Workdone = (ρVg )* d
Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m
[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]
Workdone by the pump = 1000 * 113.10 * 9.8 * 3
Workdone by the pump = 3,325,140Joules
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
Please help! Correct answer only, please! The following information matrices show how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. Which salesperson sold the most vehicle for the week described?A. Scott B. Each sold the same number of vehicles C. Kelly D. Mark
Answer: b) Each sold the same number of vehicles
Step-by-step explanation:
This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.
Kelly: 8 + 2 + 6 = 16
Scott: 7 + 8 + 1 = 16
Mark: 10 + 4 + 2 = 16
The total number of vehicles sold by each person is the same
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is AnswerPlease answer this question !! 20 points and brainliest !!
Answer:
yes, they are parallel; the general form equation differs only in the constant.
Step-by-step explanation:
Subtract y from the first equation and multiply by 2.
y -y = 1/2x -y +3
0 = x -2y +6
x -2y +6 = 0 . . . . . put in general form
Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.
This means the lines are parallel.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given by a function A(t) and the amount in Vat B is given by B(t). The two vats contain the same amount of water at t=0. You have a formula for the rate of flow for Vat A and the amount in Vat B: Vat A rate of flow: A(t)-3t2+24t-21 Vat B amount: B(t)-2t2+16t+40
(a) Find all times at which the graph of A(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum of A(t) smaller t= 1 gives a local minimum larger t= 7 l maximum
(b) Let D(t)-B(t)-A(t). Determine all times at which D(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum. (Round your times to two digits after the decimal.) xgives a Select x gives a Select smaller t- larger t=
(c) Use the fact trruntain the same amount of water at ta0 to find the formula for A(), the amount in Vat A at time t Enter a number
(d) At what time is the water level in Vat A rising most rapidly? t- hours
(e) what is the highest water level in Vat A during the interval from t=0 to t=10 hours? gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t-0 to t-10 hours? gallons per hour
(g) How much water flows into VatA during the interval from t=1 to t-8 hours? gallons
Note: The first file attached contains the clear and complete question
Answer:
a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7
A(t) has a local maximum at t=7
A(t) has a local minimum at t=1
b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74
D(t) has a local maximum at t=1.59
D(t) has a local minimum at t=7.74
c) A(t) = (-t^3) + 8(t^2) -21t + 40
d) The water level in vat A is rising most rapidly at t = 4 hrs
e) 138 gallons
f) 18 gallons per hour
g) 98 gallons
Step-by-step explanation:
For clarity and easiness of expression, the calculations are handwritten and attached as files below.
Each step is neatly expressed and solutions to each part of the question are clearly written
What is 80,000,000,000,000 in standard form (80 billion)
Answer:
8x10^13
Step-by-step explanation:
Which of the functions below could have created this graph?
Answer:
i don't know if this is right or not i did to much work to put it all down but i pretty sure it's C.
After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
Answer:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Step-by-step explanation:
We want to set up a linear function like this one:
[tex]y = mx+b[/tex]
Where y is the amount of fluid left, m the slope and b the initial amount. From the info given we know thatm = -300. And we also have the following condition:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
For each of the sequences below, find a formula that generates the sequence. (a) 4, 10, 16, 22, 28, 34, 40, . . . (b) 5, 15, 45, 135, 405, . . . (c) 10, 20, 10, 20, 10, 20, 10
Answer:
[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]
Step-by-step explanation:
[tex]6(1)-2=4[/tex]
[tex]6(2)-2=10[/tex]
[tex]5 \times 3^{(3)-1}=45[/tex]
[tex]5 \times 3^{(4)-1}=135[/tex]
[tex]5(-1^{(5)}+3)=10[/tex]
[tex]5(-1^{(6)}+3)=20[/tex]
a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)
b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹
c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is an = 10 + 10 * ((n + 1) % 2)
(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.
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A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
Suppose that it costs $200 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M = 100x-x^2 pounds ,where x is the number of people mushroom hunting on that day. Chanterelles can be sold for $60 per pound. How many more people will go mushroom hunting than is socially optimal?
Answer:
For an overall profit, we need at least 97 people to go mushroom hunting.
Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.
Step-by-step explanation:
The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.
If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x
The amount of mushroom obtained is given as
M = (100x - x²) in pounds
The selling price of 1 pound = $60
The cost of M pounds = 60M = 60(100x - x²)
= (6000x - 60x²)
At socially optimal number,
200x = 6000x - 60x²
60x² - 6000x + 200x = 0
60x² - 5800x = 0
x(60x - 5800)
x = 0 or (60x - 5800) = 0
x = 0 or x = (5800/60) = 96.67
Socially optimal number of people = 0 or 96.67
For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67
Any number above this number will result in an overall profit, and any number below it results in an overall loss.
So, for an overall profit, we need at least 97 people to go mushroom hunting.
Hope this Helps!!
Answer:
48 people
Step-by-step explanation:
When allocating resources to a particular task it is important to assign optimal units of resources.
In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.
Optimal = (M÷x)Px - 200= 0
Optimal= {(100x -x^2) ÷ x} * 60 = 200
Optimal = 6000 - 60x = 200
x= 96.666~ 97 people
However to maximise profit MTB = MTC
Socially Optimal quantity = 60(100x - x^2) -200
∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200
x = 48.33~ 48 people
So 48 more people go mushroom hunting than is socially optimal
A cognitive psychologist would like to evaluate the claim that the omega-3 fatty acids can help improve memory in normal adult humans. One group of participants is given a large dose of fish extract containing the Omega-3 (500 mg), and a second group is given a placebo containing no Omega-3 (0 mg). The researcher asks each participant to read the front page of a local newspaper thoroughly every morning and to take their prescribed dosage (of either Omega-3 or placebo) immediately afterwards. The researcher gives each participant a memory test at the end of two weeks and records how many news items each participant remembers from the past three weeks of news. Answer the following:
A) What names would you give the independent and dependent variables;
B) Is the dependent variable discrete or continuous?
C) What scale of measurement (nominal, ordinal, interval or ratio; and continuous or discrete) is used to measure the independent variable?
D) What research method is being used (experimental or observational)? Explain why you conclude that the research method is one or the other.
Answer:
(a)
Independent Variable- Dosage of Omega-3 Fatty AcidsDependent Variable - Number of news item remembered(b)Discrete
(c)Ratio Scale and Discrete Variable
(d) Experimental Method
Step-by-step explanation:
The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.
(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).
The memory test involves measuring the number of items each participant remembers from the past three weeks of news.
Therefore:
Independent Variable- Dosage of Omega-3Dependent Variable - Number of news item remembered(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.
(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.
Since the dosage is given in multiples of 50mg, it is a discrete variable.
(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
(b) Assuming the normal model can be used, determine P(x < 65.8).
(c) Assuming the normal model can be used, determine P(x 2 64.2).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) What must be true regarding the distribution of the population?
O A. Since the sample size is large enough, the population distribution does not
need to be normal.
B. The population must be normally distributed and the sample size must be large.
OC. The population must be normally distributed.
OD. There are no requirements on the shape of the distribution of the population.
Answer:
a) C. The population must be normally distributed.
b) P(x < 65.8) = 0.8159
c) P(x > 64.2) = 0.3015
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
n < 30, so the distribution of the population must be normal.
The correct answer is:
C. The population must be normally distributed.
(b) Assuming the normal model can be used, determine P(x < 65.8).
This is the pvalue of Z when X = 65.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65.8 - 62}{4.22}[/tex]
[tex]Z = 0.9[/tex]
[tex]Z = 0.9[/tex] has a pvalue of 0.8159.
So
P(x < 65.8) = 0.8159
(c) Assuming the normal model can be used, determine P(x > 64.2).
This is 1 subtracted by the pvalue of Z when X = 64.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.2 - 62}{4.22}[/tex]
[tex]Z = 0.52[/tex]
[tex]Z = 0.52[/tex] has a pvalue of 0.6985.
1 - 0.6985 = 0.3015
So
P(x > 64.2) = 0.3015
What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file