a lady on a diet measures her weight every week. the sample standard deviation is 0.6 kg, the number of measurements is 7. construct a 90% two-sided confidence interval for .
Answers
The 90% two-sided confidence interval for the lady's average weight is [57.52, 62.48] kg.
Given data: A lady on a diet measures her weight every week.
The sample standard deviation is 0.6 kg, the number of measurements is 7.
To construct a 90% two-sided confidence interval, we use the following formula:
\($$\bar{x}-t_{\frac{\alpha}{2}, n-1}\frac{s}{\sqrt{n}} \leq \mu \leq \bar{x}+t_{\frac{\alpha}{2}, n-1}\frac{s}{\sqrt{n}}$$where x\) is the sample mean.
s is the sample standard deviation.
n is the sample size.
\($t_{\frac{\alpha}{2}, n-1}$\) is the t-score.
Here, \($\alpha=1-0.90=0.10$\) (since 90% is the confidence level), and\($n-1=7-1=6$.\)
From the t-distribution table, the t-score for a 90% confidence interval with 6 degrees of freedom is
\($t_{0.05, 6}=1.943$.\)
We can substitute the given values in the formula:
\($$\bar{x}-t_{\frac{\alpha}{2}, n-1}\frac{s}{\sqrt{n}} \leq \mu \leq \bar{x}+t_{\frac{\alpha}{2}, n-1}\frac{s}{\sqrt{n}}$$$$\bar{x}-1.943\frac{0.6}{\sqrt{7}} \leq \mu \leq \bar{x}+1.943\frac{0.6}{\sqrt{7}}$$\)
Since we don't have the sample mean, we can assume that the lady's average weight is 60 kg (just for the purpose of finding the confidence interval).
\($$60-1.943\frac{0.6}{\sqrt{7}} \leq \mu \leq 60+1.943\frac{0.6}{\sqrt{7}}$$$$57.52 \leq \mu \leq 62.48$$\)
Therefore, the 90% two-sided confidence interval for the lady's average weight is [57.52, 62.48] kg.
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Related Questions
5 workers can repair the road in 9 hours. How long will it take 3
workers to do the same repairs? hours
Need just the answr please
Answers
Answer:
need to work out how long it would take 1 person first.
9 X 5 = 45
1 person will take 45 hours
45/3= 15 hours
10. you are trying to estimate the population size of a school of fish in the florida keys. the first time, you sample and mark 37 sardines. the second time around, you capture 40 sardines and 13 of them were already marked. what is the estimated population size?
Answers
Based on the information, we can infer that the estimated fish population size is 113
How to estimate the size of the fish population?To estimate the size of the fish population we can apply the Petersen method in which we must take two previous samples and apply the following formula:
N=CM/RN = estimated number of individualsC = number of individuals captured in the second captureR = number of individuals from the second capture that are markedM = number of individuals that we have marked in the first captureSo we just have to replace the values:
N=40*37/13N = 1,480/13N = 113.84Learn more about estimates in: https://brainly.com/question/17961193
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3 = y + 3*
/
6
0
9 1
Answers
8, 9, 6, 8, 8, 8, 7, 6, 9,
What is the range
Answers
Answer: 3
Step-by-step explanation:
The highest and lowest value difference is the range. 9-6=3
(a) Derive the class equation of a finite group G.
(b) Prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique.
Answers
a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.
b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.
(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).
To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:
|G| = |Z(G)| + ∑ |[a]|
where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].
The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:
Z(G) = {z in G | gz = zg for all g in G}
The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.
The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.
By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.
(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.
If a Sylow p-subgroup is normal, then it is unique:
Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.
If a Sylow p-subgroup is unique, then it is normal:
Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.
Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.
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Find an equation in point-slope form for the line having the slope m =1/3 and containing the point (-3,- 6).
Answers
What is the radius of a circle whose equation is x2 y2 8x â 6y?
Answers
The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that the general equation of the circle is x²+y²+2fx+2gy+c=0
so , the radius of the circle is calculated using the formula ,
radius = √(f² + g² - c)
On comparing the given equation with general equation
we get , the values of f as 4 and g as -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 + 9 - 21)
= √(16 + 9 - 21)
= √(25 - 21)
= √(4) = 2 .
Therefore , the radius of given circle is 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
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SOMEONE HELP ME PLEASE
Answers
Answer:
(5,-2)
Step-by-step explanation:
Evaluate the function requested. Write your answer as a fraction in lowest terms. Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 52, adjacent A C is 48, Opposite B C is 20. Find tan A. A. Tangent A = StartFraction 12 Over 5 EndFraction c. Tangent A = StartFraction 13 Over 5 EndFraction b. Tangent A = StartFraction 5 Over 12 EndFraction d. Tangent A = StartFraction 5 Over 13 EndFraction Please select the best answer from the choices provided A B C D
Answers
The value of tanA =5/12 as in trigonometry.
what is trigonometry?
The study of how the sides and angles of a right-angle triangle relate is the main focus of the field of mathematics known as "trigonometry." So, utilising trigonometric formulas, functions, or trigonometric identities, it is helpful to find the unknown or missing angles or sides of a right triangle.
solution:
As tan A = opposite/adjacent
= BC/AC
tan A = 5/12
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a triangle with a perimeter of 50 has side lengths x-1, 2x-3, and 3x "-6." what are the side lengths
Answers
The dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.
What exactly is the perimeter?Any closed shape's perimeter is just the total length of the its boundary.The perimeter of a shape is defined as the total length round the.It is the length of the outline or boundary of any two-dimensional geographic shape.The perimeters of different shape can be equal in size depending on the dimensions.For the given question,
The perimeter of the triangle is 50 units.
The three sides of the triangle is given as;
x-1, 2x-3, and 3x - 6The formula for finding the perimeter is;
Perimeter = sum of all sides.
Let 'P' be the perimeter of the triangle. Then,
P = x-1 + 2x-3 + 3x - 6
Simplifying.
P = x + 2x + 3x - 1 - 3 - 6
50 = 6x - 10
6x = 60
x = 10
For the measure of the side length, put x = 10 in the sides.
10-1 = 9 units2×10-3 = 17 units3×10 - 6 = 24 units.Thus, the dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.
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PLEASE HELP MEEEEEEEEEEEEEEEEEEEe
can u p l z help me on the one that has the colored rectangles and also number 13. number 13 is not clear tho. Niko used square tiles to make a rectangle with 2 rows and 7 tiles in each row . explain how you can find the area of the rectangle.
Answers
Answer:
See below ~
Step-by-step explanation:
For the question with colored rectangles, it asks to find the area.
The area can be found by multiplying the dimensions of the rectangle.
Blue rectangle :
A = 10 ft. x 6 ft.A = 60 ft²Green rectangle :
A = 12 cm. x 8 cm.A = 96 cm²Question 13 :
Here, we are given 2 rows and 7 columnsTake them as the dimensionsHence, area = 2 x 7 = 14 square unitsThe number of a two dollar bill i need to pay for a purchase is 9 more than the number of 5 dollar bills i need to pay for the same purchase what is the cost of the purchase?
Answers
Answer:
$60
Step-by-step explanation:
Let's say we need t $2 bills and v $5 bills.
We need 9 more $2 bills than $5 bills, so:
t = 9 + v
We also know that the amount of money in t $2 bills is 2 * t = 2t. The amount of money in v + 9 $5 bills is 5 * (v + 9) = 5v + 45. These amounts are equal:
5v + 45 = 2t
Plug v + 9 in for t in 5v = 2t + 18:
5v = 2t + 18
5v = 2 * (9 + v) + 18
5v = 18 + 2v + 18
3v = 36
v = 12
We have 12 $5 bills, so that total cost is 12 * 5 = $60.
~ an aesthetics lover
An admission ticket costs $7.50 with a 5.75% tax.
Answers
Answer:
Step-by-step explanation:
a manufacturer wishes to set a standard time required by employees to complete a certain process. times from 21 employees have a mean of 6 hours and a standard deviation of 2 hours. test if the mean processing time exceeds 5.5 hours. what is the -value of the test (round off to second decimal place)? assume normal population.
Answers
The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process
The t-value will be equal to 1.39 for the given statistics.
How to calculate the t-value?To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.
The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:
H0: µ ≤ 5.5
The alternative hypothesis is that the mean processing time is greater than 5.5 hours:
Ha: µ > 5.5
We will use a significance level of 0.05.
The formula for the t-test statistic is:
t = (X - µ) / (s / √n)
Where:
X = sample mean
µ = hypothesized population mean
s = sample standard deviation
n = sample size
Substituting the given values, we get:
t = (6 - 5.5) / (2 / √21) = 1.386
The degree of freedom for the t-test is n-1 = 20.
Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.
Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.
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What is the midpoint of the segment shown below?1010-10(-8,-7)(-7,-8) -10- A. (-15, -15)B. (-15, -15) C. (-15, -15)D. (-15, -15)
Answers
Given
The line segment with end points (-8, -7), (-7, -8).
To find:
The midpoint of the given segment.
Explanation:
It is given that,
The line segment with end points (-8, -7), (-7, -8).
That implies,
\(\begin{gathered} Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{-8+(-7)}{2},\frac{-7+(-8)}{2}) \\ =(\frac{-8-7}{2},\frac{-7-8}{2}) \\ =(-\frac{15}{2},-\frac{15}{2}) \end{gathered}\)Hence, the midpoint of the line segment is (-15/2, -15/2).
local county officials have heard reports that a service station is allowing cars 20 years and older with known violations to pass their annual safety inspection. from administrative data, they know 30% of all cars 20 years and older do not pass their annual safety inspection. to test their theory about the service station, they request records from the most recent 150 inspections of cars of this type, finding 30 of the 150 had been rejected. let p be the true rate of cars 20 years and older that do not pass their annual safety inspection from this service station. what are the implied null and alternative hypotheses local county officials are testing?
Answers
The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤ 30%.
The alternative hypothesis implied that cars 20 years or older do not pass safety inspection > 30%
The local county officials are testing a hypothesis about the proportion of cars 20 years.
And older that do not pass their annual safety inspection at the service station.
The null hypothesis and alternative hypothesis can be stated as follows,
Null hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤ 30%.
Alternative hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.
The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.
And that the rejection rate of 30% is consistent .
With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.
The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.
And that the rejection rate is lower than the true rate of cars 20 years .
And older that do not pass their annual safety inspection at the service station.
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what is 25% off $27
Answers
Answer:
6.75 $
Step-by-step explanation:
25%
= 25 / 100
= 1 / 4
25% of $ 27
= ( 1 / 4 ) x ( 27 )
= ( 1 x 27 ) / 4
= 27 / 4
= 6.75 $
Answer:
$20.25
Step-by-step explanation:
If Alex can do 15 jumping jacks in 20 seconds, how many can he do in 2 minutes
Answers
Select the correct function and value on the image.Suppose your soccer coach is ordering duffel bags online for your team. The online store charges$16.49 per bag, plus $10.50 for shipping and handling of the order. Suppose x is the number of bagsordered and g(x) is the total cost of the bags. Select the function that models the relationship. Then,select the cost of buying 12 bags.g(x) = 16.49x + 10.50g(x) = 16.49x + 10.50xg(x)= 10.50x + 16.49g(x)= 16.49x 10.50OinINTL
Answers
We are asked to model the given problem using a function in the form of y=mx +c
In this case, our "y" will be the total amount spent while m as the co-efficient of x will equal the amount spent per bag. Lastly the $10.5 dollars that needs to be spent per order has been given independent of how many bags are ordered. This is our value for "c".
Correct option: g(x) = 16.49x + 10.5
We will then calculate the cost of buying 12 bags by substituting this into our equation:
g(12) = 16.49(12) + 10.5
= $208.38
0.3(4 − x) = x − 1.4?
Answers
Answer:
x is equal to 2
Step-by-step explanation:
simplify the equation
distribute the 0.3
0.3*4-0.3x=x-1.4
1.2-0.3x=x-1.4
get x by itself on one side
1.2+1.4=x+0.3x
simplify
2.6=1.3x
2=x
The last one is $30 which one ?
Answers
Answer:
it may be 30
Step-by-step explanation:
becasue 6x2 is 12 half hour $3 and kayak 15 all that is 30
Answer:
it's 30
Step-by-step explanation:
15 + 6 + 6 + 3
15+15
15 was the down payment, plus six dollars for the hours he was there and then three dollars for the half hour.
NEED HELP DUE TODAY!!!! GIVE GOOD ANSWERS PLEASE!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
Answers
Answer:the triangles are similar to each other by AA rule and EF = 8.
Step-by-step explanation:
the triangles are similar to each other by AA rule and EF = 8.
this should help if wrong sorry im in middle school so
On a hot summer day, Nora and her friends decided to have a water fight. They threw water balloons for 1 hour. When all the water balloons were gone, they sprayed water with hoses for 30 minutes. The water fight ended at 1:45 P.M. when Nora's dad showed up with ice cream. What time did the water fight start?
Include A.M. or P.M. in your answer (for example, 11:58 A.M.).
will give brainilest
Answers
Answer: 12:15 pm
Step-by-step explanation:
They had a balloon fight for 1 hour
They played in the hose for 30 minutes
The water fight ended at 1:45 pm minus 1 hour 30 minutes if play = 12:15 pm start time
A truck can be rented from Company A for $60 a day plus $0.30 per mile. Company B charges $30 a day plus $0.40 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for
Company A and Company B are the same.
Answers
Answer:
300 miles
Step-by-step explanation:
The total cost function for Company A is C(x) = $60 + ($0.30/mi)x.
That for Company B is C2(x) = $30 + ($0.40/mi)x
To answer this question, we equate C(x) and C2(x):
$60 + ($0.30/mi)x = $30 + ($0.40/mi)x
Combining the terms, we get:
$60 = $30 + ($0.10/mi)x
Next we combine the constant terms, obtaining:
$30 = ($0.10/mi)x
This works out to x = 300 miles
The number of miles in a day at which the rental costs for Company A and Company B are the same is thus x = 300 miles
PLEASE HURRY THIS IS DUE IN 2 HOUR!! the table at the right shows the fee for overdue books at the library based on the number of weeks the book is overdue write a function rule to find the fee for a book that is x weeks overdue
Answers
please find answer.
Answers
Answer:
Again, the answer is (1,-2)
Step-by-step explanation:
Substitute the values
Solve for x. For the equation
Answers
Answer:
x=y/m - b/m
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
La población actual de México es de aproximadamente 126,000,000 dehabitantes. Si la población crece a una tasa de 2.5% anualmente, ¿cuál serála población en el año 2036?
Answers
Answer:
182,485,569 habitantes
Step-by-step explanation:
126,000,000 (1 + 0.025)^15
= 182,485,569
The Tober family built a square deck with an area of 75 m'. The length of one
side is between which two whole numbers
Answers
Answer:
Between 8 and 9
Step-by-step explanation:
The square root of 75 is about 8.6
Therefore the answer is between the number 8 and 9.
How do you find the surface area of an acute triangle?
Answers
The area of the acute triangle can be found by the formula: area of acute triangle = (1/2) × b × h.
According to Pythagoras theorem the triangle is termed as acutely angled if the square of its longest side is less than the sum of the squares of two other smaller sides. Let a, b, and c are the length of sides of a triangle, where side "a" is the longest, then the given triangle is acutely angled if and only if a^2 < b^2 + c^2.
The area of the acute triangle can be calculated by the formula:
area of acute triangle = (1/2) × b × h
b = base, and
h = height
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