Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2266 = 22.66% probability that the sample mean is greater than 63.
b) 0.1587 = 15.87% probability that the sample mean is less than 56.
c) 0.6147 = 61.47% probability that the sample mean is between 56 and 63.
In a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 60, thus [tex]\mu = 60[/tex].Standard deviation of 12, thus [tex]\sigma = 12[/tex].Sample size of 9, thus [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 63, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 60}{4}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a p-value of 0.7734.
1 - 0.7734 = 0.2266
0.2266 = 22.66% probability that the sample mean is greater than 63.
Item b:
This probability is the p-value of Z when X = 56, so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 60}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that the sample mean is less than 56.
Item c:
This probability is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 56.
These p-values were found in the previous items, so:
0.7734 - 0.1587 = 0.6147
0.6147 = 61.47% probability that the sample mean is between 56 and 63.
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PLEASE SHOW YOUR WORK
FIRST TO ANSWER GETS BRAINLIEST!
Answer:
Carlton: 731 feet tall
Burj Khalifa: 2716 feet tall
Q1 Tower: 1059 feet tall
The Shard: 1017 feet tall
Willis Tower: 1450 feet tall
Gran Torre: 984 feet tall
(note: this is all rounded up answers)
Work:
223 x 3.28 = 731
828 x 3.28 = 2716
323 x 3.28 = 1059
310 x 3.28 = 1017
442 x 3.28 = 1450
300 x 3.28 = 984
irreducible fraction of -72/80 please
Answer:
Step-by-step explanation:
-72/80 = -36/40 = -18/20 = -9/10
PLEASE HELP!!! i don’t know the answer and it’s due tmr!!
look at the image of the graph
Express the fraction 2/3, 3/4,5/6
Answer:
The required fractions for 2/3, 3/4, and 5/6 with a denominator of 12 are 8/12, 9/12, and 10/12
Answer:
8/12, 9/12, and 10/12
Step-by-step explanation:
Please answer this hurry!!!!!
PLEASE HELP ITS MATH THANK YOUUUU
Michael can clean the store in 6 hours. Together him and Lebron can clean the same store in 2 hours. How long would it take for Lebron to clean the store alone?
Answer:
4 hours.
Step-by-step explanation:
The difference between 6 and 2 is 4.
Urgent!!!⚠️⚠️⚠️⚠️⚠️⚠️⚠️It takes 46 pounds of seed to completely plant a 5 acre field how many pounds of seeds are needed per acre
Answer:
9.2 pounds per acre
Step-by-step explanation:
Divide 46÷5, 9.2
46 represents the pounds of seeds
5 represents how many acres in the field
At the end of the night, a restaurant had 3/4 of a large birthday cake left over. The 5 employees each took home the same amount of leftover cake. How much cake did each employee take home?
Answer:
3/20
Step-by-step explanation:
This is a division question.
The equation is 3/4 ÷ 5 or, to simplify this, 3/4 ÷ 5/1.
When you divide fractions you have to flip the second number and multiply the two fractions.
So, you have to do 3/4 x 1/5 which is 3/20.
Thus, the answer is 3/20.
Good luck!
Calvin works at a pizza place making pizzas. If he is working alone, he can make an average of 15 3/4 per hour. If he works with his friend Megan, he tends to get distracted, and his rate falls by 1/2 per hour. How many pizzas can Calvin make in a 8- hour shift with Megan?
Explain the operations that will be needed to solve this problem, ans then solve it.
The fraction 1/2 converts to 0.50 in decimal form.
The mixed number 15 & 3/4 is the same as 15.75
If Calvin is distracted, then he makes 15.75-0.50 = 15.25 pizzas per hour on average.
Multiply by 8 to find the total number of pizzas possible.
8*15.25 = 122
Answer: Calvin can make 122 pizzas overall if he is distractedCalvin can make 122 pizzas in an 8-hour shift with Megan.
Since Calvin works at a pizza place making pizzas, and if he is working alone, he can make an average of 15 3/4 per hour, but if he works with his friend Megan, he tends to get distracted, and his rate falls by 1/2 per hour, to determine how many pizzas can Calvin make in a 8-hour shift with Megan, the following calculation must be performed:
Rate of pizzas made x number of hours = Total number of pizzas (15 3/4 - 1/2) x 8 = X (15.75 - 0.5) x 8 = X 15.25 x 8 = X 122 = X
Therefore, Calvin can make 122 pizzas in an 8-hour shift with Megan.
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Jenelle bought a home for $320,000, paying 24% as a down payment, and financing the rest at 5% interest for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she will spend on this home. Include the down payment in your answer. $
She paid $ 76,800 as down payment, the original amount financed was $ 243,200, her monthly payment was $ 2,919.71, and the total amount she will spend on this home is $ 1,127,896.38.
Given that Jenelle bought a home for $ 320,000, paying 24% as a down payment, and financing the rest at 5% interest for 30 years, to determine how much money did Jenelle pay as a down payment, what was the original amount financed, what is her monthly payment, and the total amount of money she will spend on this home, the following calculations must be made:
320,000 x 0.24 = Down payment 76,800 = Down payment 243,200 x 1.05 ^ 30 = X 243,200 x 4.32 = X 1,051,096.38 = X 1,051,096.38 / (30 x 12) = X 2,919.71 = X 1,051,096.38 + 76,800 = 1,127,896.38
Therefore, she paid $ 76,800 as down payment, the original amount financed was $ 243,200, her monthly payment was $ 2,919.71, and the total amount she will spend on this home is $ 1,127,896.38.
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In 1950, scientist estimated a certain animal population in a particular geographical area to be 6400 in 2000, the population had risen to 7200. If this animal population experiences the same % increase over the next 50yrs what will be approximate population be?
Answer:
8,100
Step-by-step explanation:
7,200 - 6,400 = 800 increased in 50. Years
What percentage is 800 of 6,400 (%/100 = is/of)
x/100 = 800/6400 (cross multiply)
(800*100)/6400 = 12.50%
(12.50 * 7200)/100 = 900 increased
7,200 + 900 = 8,100
The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car
and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different
mileage and determines each car's price using a used car website. The analysis is given in the computer output.
Predictor Coef SE Coef t-ratio
р
Constant 2415712 2164.1 2.965
0.046
Mileage
-0.181 0.024 5.377
0.000
s = 3860.7
R-S = 68.0%
R-Sq (Adi) = 69.59
Using the computer output, what is the value of the coefficient of determination?
00.46
0.68
N
0.70
0.82
The value of the coefficient of determination is gives the percentage of the variation which is explained by the regression line. The value of the coefficient of determination is the R² value which is 68%.
The Coefficient of determination is the proportion of change in the regression model caused by the regression line. From the computer output, the coefficient of determination is denoted as R² ; which is given as 0.68 Expressing the value as a percentage ; 0.68 × 100% = 68%Therefore, the coefficient of determination is 0.68
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Answer:
B) .68
Step-by-step explanation:
EDGE
x cube + 1 ÷ x squared -x+1
Jina,tony, and Henry have a total cost of $70 in their wallets. Tony has 2 times what Henry has. Henry has $10 more than Jina. How much do they have in their wallets?
Answer:
Jina has $10,
Tony has $40,
and Henry has $20
Step-by-step explanation:
So if we use a little bit of algebra, let's say
Jina's amount = a.
Henry has $10 more than Jina, so that would make Henry's amount: a + 10. Tony has two times more dollars than Henry, so multiply Henry's amount
(a + 10) by 2, and you get: 2(a + 10).
Here's to make things easier on the eye for you:
Jina's amount = a
Henry's amount = (a + 10)
Tony's amount : 2(a + 10)
Next, form an equation by adding each of the three's amounts together:
Jina's amount + Henry's amount + Tony's amount
= a + (a + 10) + 2(a + 10)
= a + a + 10 + 2a + 20
(add the a's together and the numbers together. Then, put the total amount, $70, on the other side of the equation)
4a + 30 = 70
(subtract 30 from both sides of the equation: 4a + 30 - 30 = 70 - 30)
= 4a = 40
(and now, simplify by dividing by 4)
a = 10
Substitute 10 for a:
Jina: a = $10
Henry = (a + 10) = (10 + 10) = $20
Tony = 2(a + 10) = 2(10 + 10) = 2(20) = $40
Add them all up if you want to check if its correct:
$10 + $20 + $40 = 70$ ✔
Sorry if this explanation was a bit long, I hope you understand ^^.
Choose the pythagorian triplet with the smallest number as 10.
a) 24, 26, 10
b) 10, 6, 8
c) 10, 16, 18
d) 10, 18, 20
Answer:
b
Step-by-step explanation:
pls give brainliest hope helpful
Jonah found that it took him 10 minutes to do 5 math problems. If he uses this information, what should be his estimation on how long it will take him to do 32 math problems?
We can round 32 down to 30.
10 minutes for 5 math problems is the same as 2 minutes for 1 math problem. Therefore, we can estimate that it will take Jonah approximately 60 minutes to do 32 math problems.
Hope this helps!! :)
The value of sin 240° is
Answer:
-0.5879
......................................
Answer:
-0.866
Step-by-step explanation:
or -(√3/2)... same thing just different format. Hope this helps
Please help for brainliest !!
Answer:
i do bellieve it is c
Step-by-step explanation:
Can someone please help me out?
I know that by using length times width, the first rectangle is equal to 25 in^2 and the second rectangle is equal to 24 in^2. I just don't understand why they can both be right.
Answer:
Minh says that the rectangle on the left in Fig- ure 11.12 is larger than the one on the right, Sequoia says the rectangle on the right is larger than the one on the left. Explain why Minh and Sequoia can both be right. 25 Figure 11.12 Two rectangles. 24
Solve for X
Marking anybody who got it right the brainliest
Answer:
198°Step-by-step explanation:
We see angles P and R marked to be same with P having the angle measure indicated.
We assume the Q is the right angle, otherwise the given info is not enough to find the answer.
Added segments parallel to PQ and QR. See the picture.
The angle x is partitioned as:
Right angle and two complementary angles, one with P and one with R.Then its measure is:
90° + 2(90° - 36°) = 198°what is the expanded form of 203,574
Expanded Notation Form:
203,574 =
200,000
+ 0
+ 3,000
+ 500
+ 70
+ 4
Expanded Factors Form:
203,574 =
2 × 100,000
+ 0 × 10,000
+ 3 × 1,000
+ 5 × 100
+ 7 × 10
+ 4 × 1
Expanded Exponential Form:
203,574 =
2 × 105
+ 0 × 104
+ 3 × 103
+ 5 × 102
+ 7 × 101
+ 4 × 100
The slope is negative in the graph as you move from left to right the line of the graph is going
Answer:
Down
Step-by-step explanation:
The line slants downward from left to right if the slope is negative.
Se le conoce como medidas o parámetros que se sitúan hacia el centro de un conjunto de valores,
con el objetivo de analizar un análisis profundo de los resultados
Las medidas o parámetros que se sitúan hacia el centro de un conjunto de valores, con el objetivo de analizar un análisis profundo de los resultados, son denominadas "medidas de tendencia central".
Una medida de tendencia central da una impresión del centro de una cantidad de datos o una distribución. Dependiendo de la medida de centro utilizada, el centro puede significar el centro de los datos o la distribución, o el lugar más probable donde se encuentran la mayoría de los datos.
Por tanto, una medida de centro da una impresión de los datos o la distribución en un número y, a veces, también se utiliza como un resumen de un solo número de los datos o la distribución. Las medidas conocidas del centro son la media aritmética y geométrica, la mediana, la moda y el centro del rango (el valor exactamente entre los valores mínimo y máximo).
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Answer:
Generalmente, los refugiados son personas que están fuera de s volver allí porque temen daños personales graves.
Step-by-step explanation:
Generalmente, los refugiados son personas que están fuera de s volver allí porque temen daños personales graves.
The surface area of a piece of paper is 345 cm2. Use the fact that 10 mm = 1 cm to convert this area to mm2
Step-by-step explanation:
345cm²=34500mm²
:;
cm in mm(*10)
cm² in mm²(*100)
cm³ in mm²(*1000)
I'd appreciate the brainliest
HELP I DONT WANT A 0000
Step-by-step explanation:
=(5+8)hours
=12hours.
Juanita is tying ribbon on gift bags. She has 24 feet of ribbon and each gift bag uses 0.75 foot of ribbon. The function
r = 24 -0.75g represents the amount of ribbon r Juanita has left after tying ribbon on g gift bags. Find the zero of the function. Describe
what this value means in the context of this situation
The zero of the function is at ___. This represents that after tying ribbon on ____ gift bags, Juanita will have ____ feet of ribbon left.
The zero of the function is at 32 gift bags. This represents that after tying ribbon on 32 gift bags, Juanita will have zero feet of ribbon left.
According to the question;
The function r = 24 -0.75g represents the amount of ribbon r Juanita has left after tying ribbon on g gift bags.The zero of the function is at, r = 0.
Therefore;
0 = 24 -0.75gg = 24/0.75g = 32.This value means that after tying 32 gift bags, Juanita will have zero feet of ribbon left.
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John and Jill collect 280 stamps. Out of this John collected three time as many as
Jill. How many stamps did Jill collected?
Answer:
Jill collected 70 Stamps
John collected 210 Stamps
Step-by-step explanation:
280/4=70
Please allow me to know if my answer helped you with a thank you!
<3Miss Hawaii
Help with Algebra 2, forgot how to do it
Answer:
[tex]f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6[/tex]
Simplify
1/2 + 2/5
A) 1/10
B) 2/7
C) 3/7
D) 9/10
Answer:
D) 9/10Step-by-step explanation:
Add up as fractions:
1/2 + 2/5 = Common denominator is 2*5 = 105/10 + 4/10 = 9/10Option D
Option D
