1)
On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with ? = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of ?.
(a) Assuming this to be the case, if a sample of 49 modified bars resulted in a sample average yield point of 8459 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.)
( ? , ? )
(b) How would you modify the interval in part (a) to obtain a confidence level of 98%? (Round your answer to two decimal places.)
2)
An article reported that for a sample of 48 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.85.
(a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
( ? , ? )
(b) Suppose the investigators had made a rough guess of 170 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 47 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
Answers
1) On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar,
a) 90% CI for the true average yield point of the modified bar is 8459 +/- 23.5
b) 98% CI for the true average yield point of the modified bar is 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
a) 95% (two-sided) confidence interval for true average CO2 level in the population is 654.16 +/- 185.0632
b) Sample size is 12.
What is Confidence Interval ?The confidence interval for the population mean is constructed about the sample mean i.e. sample mean lies at the center of the interval.
1) The yield point of a particular type of mild steel-reinforcing bar is normally distributed with
Sample size,n = 49
Sample mean , X-bar = 8459 lb,
Standard deviations, σ = 100
We have to compute 90% CI for the true average yield point of the modified bar.
α = 1 - 90% = 1- 0.90 = 0.10
a)From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₅ level of significance is 1.645.
Confidence interval formula ,
X-bar +/- Zα/2(σ /√n)
90% CI for the true average yield point of the modified bar, is
8459 +/- 1.645(100/√49)
=> 8459 +/- 1.645(100/7)
=> 8459 +/- 1.645(14.2857) = 8459 +/- 23.5
b)
Now, we have to compute 98% CI for the true average yield point of the modified bar.
α = 1 - 98% = 1 - 0.98 = 0.02
From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₁ level of significance is 2.326.
Then, Confidence interval is,
CL = 8459 +/-2.326(100/√49)
= 8459 +/- 1.645( 14.285) = 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
Sample size, n = 48
Sample mean , X-bar= 654.16
standard deviations, σ = 162.85
a) We have to calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level. α = 1 - 0.95 = 0.05 ; α/2 = 0.025
From Standard Normal Table, the critical value at the Zα/2 = Z0.025 level of significance is 1.96
95% (two-sided) confidence interval for true average CO2 level is 654.16 +/- 1.96(654.16 /√48)
= 654.16 +/- 1.96(94.42)
= 654.16 +/- 185.0632
b) The distance between the two ends limits of the interval is known as the width of the interval and it is twice the margin of error.
We have width of the interval = 47 ppm
so, Margin of error , MOE = 94
Significance level, 95%
we have to determine sample size
Margin of error formula is
MOE = Zα/2(σ/√n)
where n is sample size.
94 = 1.96 (162.85/√n)
=> √n = 162.85 × 1.96/94 = 3.39559574468
=> n = 11.53 ~ 12
Hence, sample size is 12..
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Related Questions
Solve x2 = −169 im not that good at math
Answers
Answer:
Hi there
Your answer is:
13i
Step-by-step explanation:
Find the square root of √-169
We do i as coefficient to get rid of negatives
√169 is 13
Hope this helps
simplify each algrebraic expression. drag tiles to correct boxes to complete the pairs.
-5x-2 5x+2 5x-2 -5x+2
Answers
(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.
(b) The algebraic expression, 5x -2 - (5x + 2) is simplified as -4.
What is the simplification of the algebraic expression?The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.
The given algebraic expressions are;
-5x - 2 + 5x + 2
5x -2 - (5x + 2)
The first algebraic expression is simplified as follows;
-5x - 2 + 5x + 2
collect similar terms;
(-5x + 5x) + (-2 + 2)
= 0 + 0
= 0
The second algebraic expression is simplified as follows;
5x - 2 - (5x + 2)
= 5x - 2 - 5x - 2
collect similar terms;
= (5x - 5x) + (-2 - 2)
= 0 - 4
= - 4
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Use a net to find the surface area of the prism.
A. 426m2
B. 213m2
C. 306m2
D. 336m2
Answers
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
The dimensions for this problem are given as follows:
5 m, 12 m and 9 m.
Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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Solve b + 6 < 14.
Write your answer in set builder notation
Answers
b + 6 - 6 < 14 - 6
This simplifies to:
b < 8
Therefore, the solution to the inequality is the set of all numbers b that are less than 8.
In set builder notation, we can represent this solution as:
{ b | b < 8 }
A calf raiser mixes a batch of milk replacer for 15 calves. Each calf gets two
quarts of milk replacer. If the calf raiser uses 960 oz. of replacer and needs to
add 34 as much water as milk replacer, how many ounces of water does she need?
Answers
Answer:
The calf raiser uses 960 oz of milk replacer for 15 calves, so each calf gets 960 oz / 15 = 64 oz of milk replacer.
To convert this to quarts, we need to divide by 32 (since there are 32 oz in a quart)
64 oz / 32 oz/quart = 2 quarts
Each calf gets 2 quarts of milk replacer and the calf raiser needs to add 34 as much water as milk replacer
So the total amount of water she needs is 2*34 = 68 quarts
To convert the quarts of water to ounces we need to multiply by 32 (since there are 32 oz in a quart)
68 quarts * 32 oz/quart = 2176 oz of water.
So the calf raiser needs 2176 ounces of water to mix with the milk replacer for 15 calves.
A one-tailed hypothesis test with the t statistic Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of disgust. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
The null hypothesis is that your sample of children with antisocial tendencies would have no more difficulty recognizing emotion than the general population of 16-year-olds. Stated using symbols:_________. This is a __________ tailed test. Given what you know, you will evaluate this hypothesis using a________ statistic.
Answers
Step-by-step explanation
The answers in bold is what was required from the question.
the null hypothesis using symbol:-
H₀ : μ = 11.80
the alternative hypothesis using symbol:-
H₁: μ ≠ 11.80
This is a one tailed test. Given what you know, you will evaluate this hypothesis using a t test statistic.
Alpha level = 0.05
Sample size = n
Degree of freedom = n-1 = 40-1 = 39
To use the t distribution we will have to find the critical value from the t table this value is 1.685
But the question does not have sample mean and sample standard deviation. So I was unable to solve for the standard error
Find the LCM of 30 and 22. LCM = ___a0
Answers
Answer:
The answer would be 330:)
Step-by-step explanation:
How to Find LCM by Listing Multiples :
List the multiples of each number until at least one of the multiples appears on all lists
Find the smallest number that is on all of the lists
This number is the LCM
RLY hope this helps:) If so, can I have brainliest?
Answer:
The LCM of 30 and 22 is 330
Step-by-step explanation:
22 x 15 = 330
30 x 11 = 330
A recipe uses 5 cups of flour for every 2 cups of sugar.
How much sugar is used for 1 cup of flour?
How much flour is used for 1 cup of sugar?
How much flour is used with 7 cups of sugar?
How much sugar is used with 6 cups of flour?
Answers
Answer:
2.5
Step-by-step explanation:
5 divided by 2= 2.5
Answer:
2.5
Step-by-step explanation:
The first equation of a system of equations is y = -3x + 2. The graph of the system has no solution. Write a possible second equation for the system.
Answers
Answer:
see below.
Step-by-step explanation:
For a system of equation to not have a solution, the pair of lines will never intersect. For two lines to never intersect, their slopes will be parallel.
The second equation can be as simple as y = -3x.
The only equation it cannot be with a slope of -3 is y = -3x + 2. This is because that is the same equation and will therefore have an infinite number of solutions.
Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
I NEED HELP PLEASE IM IN A TEST RN IF YOU GIVE ME THE CORRECT ANSWER I WILL GIVE U 70 PONITS
Answers
Sara and Ashton both have the same number of comic books after 10 months
How to determine when they both have the same number of books?From the question, we have the following parameters that can be used in our computation:
Sara
Initial = 12 comic books
Books at the fourth month = 20
Ashton
Initial = 2 comic books
Books each month = 3
The equations can be represented as
Total number of books = Initial + Books each month * Number of months
Rewrite as
y = Initial + Books each month * x
For Ashton, the equation is
y = 2 + 3x
For Sara, we have
y = 12 + Books each month * Number of months
So, we have
20 = 12 + Books each month * 4
This gives
Books each month = 2
So, the equation is
y = 12 + 2x
Substitute y = 2 + 3x in y = 12 + 2x
2 + 3x = 12 + 2x
Evaluate the like terms
x = 10
This means that
Number of months = 10
Hence, the number of months is 10
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Complete question
Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
Calculate when they both have the same number of books
While chasing its prey, a cheetah is running slowly and then increases its speed by 42.5 miles per hour to reach a top speed of 70 miles per hour. What is the cheetah's initial speed?
42.5 miles per hour
or
112.5 miles per hour
or
27.5 miles per hour
or
35.5 miles per hour
Answers
Answer: 27.5 miles per hour
Step-by-step explanation: 70 - 42.5 = 27.5
What is the perimeter of the shaded figure?
Answers
En una ciudad de 5000 habitantes, la tasa diaria
de infección con un virus de la gripe varia directamente con el producto de
personas infectadas y el número de personas no infectadas. Cuando se han
infectado 1000 personas, la gripe se esparce a razón de 40 nuevos casos por día.
¿Para qué número de personas infectadas, la tasa diaria de infección es la
máxima?
Answers
According to the information, the maximum infection rate is: k * 2500 * (5000 - 2500) = 6250k = 40
How to calculate for what number of infected people, the daily infection rate is the maximum?To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:
infection rate = k * (infected people) * (uninfected people)where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:
infection rate = k * x * (5000 - x)To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:
d(infection rate)/dx = k * (5000 - 2x) = 0This implies that 5000 - 2x = 0, and therefore:
x = 2500Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.
However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:
infection rate = k * 2500 * (5000 - 2500) = 6250kIf the infection rate is 40 new cases per day, we have:
40 = 6250kwhich implies that:
k = 0.0064Therefore, the maximum infection rate is:
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On a map, the scale shown is 1 inch : 5 miles. If
a wildlife refuge is 50 square miles, what is the
area of the refuge on the map?
Use the proportion to solve for x.
1 in. 2
25 mi2
x in. ²
50 mi²
Cross
multiplication
can help!
=
The area of the wildlife refuge is [?] square
inches on the map.
Enter
Answers
Answer:
Step-by-step explanation:
6
A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class. Write an equation that represents the total cost of the membership.
Answers
The equation that represents the total cost of the membership will be y = 5x + 265.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.
Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,
y = 5x + 265
The equation that represents the total cost of the membership will be y = 5x + 265.
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Two intersecting segments form the diagonals of a quadrilateral. What additional information do you need to know about the diagonals to prove that a quadrilateral is a parallelogram
Answers
Answer:
B. They must bisect each other
Step-by-step explanation:
Found the answer on quizziz
(SAT Prep) Find the value of x
Answers
X=25°
................
Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths of the missing sides of figure B
A 4 sided polygon, labeled A, with sides labeled as follows: left, 15, top, 12, right, 18, bottom, 20. A smaller, 4 sided polygon, labeled b, oriented the same way, has left side labeled: 3.
Answers
Answer:
Left 3, top 2.4, right 3.6, bottom 4. Scale factor 5
Step-by-step explanation:
Madison and Cindy have a combined age of 65 Cindy is 20 less than four times Madison's age how old are Madison and Cindy
Answers
Cindy's age is 40 years and Madison's age is 17 years.
What is an expression?Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Madison and Cindy have a combined age of 65 Cindy is 20 less than four times Madison's age. The age will be calculated by using the information.
C + M = 65
C = 4M - 20
4M - 20 + M = 65
5M = 65 + 20
5M = 85
M = 85 / 5
M = 17 years
Therefore, Cindy's age is 40 years and Madison's age is 17 years.
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Given the drawing as shown below and that pllq. Which of the following cannot be supported by the evidence shown? Worth 10 points
Answers
The relation that can not be supported by the evidence in the image is option B
What happens when a transversal cuts a parallel line?
Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.
Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.
Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.
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can someone please help me with this?!
Answers
Answer:
26) Let the first number be x.
Sum of three consecutive even numbers:
\(x+(x+2)+(x+4)=-84\)
\(x+x+2+x+4=-84\\\)
\(3x+6=-84\)
Subtract 6 from both sides:
\(3x+6-6=-84-6\)
\(3x=-90\)
Divide both sides by 3:
\(\frac{3x}{3}=\frac{-90}{3}\)
\(x=-30\)
To find the other two numbers, add 2 and 4 respectively:
\((-30+2=-28)(-30+4=-26)\)
27) Let the first number be x.
Sum of three consecutive odd integers:
\(x+(x+2)+(x+4)=141\)
\(3x+6=141\)
Subtract 6 from both sides:
\(3x+6-6=141-6\\3x=135\)
Divide both sides by 3:
\(\frac{3x}{3}=\frac{135}{3}\\x=45\)
To find the other two numbers, add 2 and 4 respectively:
\((45+2=47)(45+4=49)\)
28) Let the first number be x.
Sum of four consecutive integers:
\(x+(x+1)+(x+2)+(x+3)=54\)
\(4x+6=54\)
Subtract 6 from both sides:
\(4x+6-6=54-6\\4x=48\)
Divide both sides by 4:
\(\frac{4x}{4}=\frac{48}{4}\\x=12\)
To find the other three numbers, add 1, 2 and 3 respectively:
\((12+1=13)(12+2=14)(12+3=15)\)
29) Let the first number be x.
Sum of four consecutive integers:
\(x+(x+1)+(x+2)+(x+3)=-142\)
\(4x+6=-142\\\)
Subtract 6 from both sides:
\(4x+6-6=-142-6\)
\(4x=-148\)
Divide both sides by 4:
\(\frac{4x}{4}=\frac{-148}{4}\\x=-37\)
To find the other three numbers, add 1, 2 and 3 respectively:
\((-37+1=-36)(-37+2=-35)(-37+3=-34)\)
A class has 7 boys and 10 girls. Select all associated ratios for this class.
10:3
7:3
17:5
7:17
10:7
10:17
7:10
3:7
Answers
Answer:
7:10
Step-by-step explanation:
…..
because boys number is 7 and girl number is 10 so
Calvin practiced converting standard notation to scientific notation by completing the 10 problems
in the table shown. Unfortunately, his teacher noticed Calvin made mistakes on 7 out of the 10
problems. Find his mistakes and correct them in the second table below.
STANDARD NOTATION
SCIENTIFIC NOTATION
1) 76,450,000
7.645 x 10
2) 0.000327
3.27 x 104
3) 34,000
3.4 x 104
4) 116,000,000,000
1.16 x 10°
5) 0.024
24 x 10
6) 2,800
2.8 x 10
7) 100
1 x 10
8 0.0000099
9.9 x 10
9 C00,000
9 x 10
10) 0.00635
63.3 x 10
I
Answers
Answer/Step-by-step explanation:
The 7 problems Calvin made mistakes in are as follows:
1. 76,450,000
We are moving the decimal point to our left by 7 decimal places. Therefore, the exponent of 10 should be 7 not 8.
The correct scientific notation = \( 7.645*10^7 \)
2. 0.000327
We move the decimal point to our right by 4 decimal places. Since we are counting to our right, the exponent of 10 should be -4 not 4.
The correct scientific notation = \( 3.27*10^{-4} \)
4. 116,000,000,000
Number of decimal places moved to our left = 11
The exponent of 10 should be 11 not 9.
The correct scientific notation = \( 1.16*10^11 \)
5. 0.024
Number of decimal places moved to our right = 2
Since we are moving to our right, exponent of 10 = -2.
Calvin made a mistake here by not placing a decimal point in the first number after the last 0 to our right.
The correct scientific notation = \( 2.4*10^{-2} \)
7. 100
There are just 2 zeros.
Therefore, the exponent of 10 = 2 not 3.
correct scientific notation = \( 10^2 \)
9. 900,000
Number of decimal places moved to our left = 5
Since we are moving to the left, the exponent of 10 = 5 not -5
The correct scientific notation = \( 9*10^5 \)
10. 0.00633
Number of decimal places moved to our right = 3
The exponent of 10 = -3
Calvin made a mistake by wrongly placing the decimal point.
The correct scientific notation = \( 6.33*10^{-3} \)
Can anyone help pls for both questions and I don’t understand what they mean by the solution!
Answers
Answer:
Step-by-step explanation:
b-20-4b
5b=-20
b=-4
He used 4 beads for each necklace.
The second one is 28
Because:
You have a total of beads at the start wich is represented by b
You subtract 20 beads from this total, so b-20
You then divide the rest into 4 necklaces, so (b-20)/4
For the second one, the equation is time left=45-6j-2s, and the answer in this case is 17 minutes
Because:
You start with a total of 45 minutes
She does 6 laps, and the time for these laps are represented by j
She does 2 stretches, and the time for these stretches are represented by s
You now have your equation: 45-6j-2s
Since the time required for a lap is 3 minutes and the time for a stretch is 5 minutes, you replace j and s by 3 and 5 respectively.
Giving you 45-6(3)-2(5)= 17 minutes left
what does new thousand mean?
Answers
We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.
What is a thousand?A thousand is a number that denotes the sum of 1,000 units or ten hundreds.
The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."
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A calibrated measurement system is used to quantify an analog measurand. A measurement standard with a value of 5.3 units was measured 10 times. The average and standard deviation of the resulting measurements are 5.4 and 0.4, respectively. What is the amount of bias error
Answers
A bias error is the difference between the expected value and the true value of the data.
The bias error of the given data is 0.1
Solution:Bias Error= Expected Value- True Value
The mean is taken as the expected value.Bias Error= 5.4-5.3
Bias Error= 0.1
The bias error is also known as systematic error.
The bias error can also be understood by the following.
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The probability that a high school senior wins a prestigious scholarship is 0.13. The probability that a high school senior plays a varsity sport is 0.22 . If the probability that someone plays a varsity sport given that they won the scholarship is 0.55 , then what's the probability that someone wins the scholarship given that they play a varsity sport?
Answers
Answer:
0.325
Step-by-step explanation:
Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport
Given
P(A) = 0.13P(B) = 0.22P(plays a varsity sport given that they won the scholarship)= P(B|A) = 0.55We are asked to find P(wins the scholarship given play a varsity sport) = P(A|B)The formula for conditional probability is
\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\\\\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)}\)where P(A ∩ B) is the probability of both A and B occurring togetherRewriting the above two equations we get
\(P(A \cap B) = P(A|B)P(B) = P(B|A)P(A)\)
→ \(P(A|B)P(B) = P(B|A)P(A)\)
Plugging in known probabilities,
\(P(A|B) (0.22) = P(0.55)(0.13)\)
\(\begin{aligned}P(A|B) & = \dfrac{0.55 \times 0.13}{ 0.22 }\\& = 0.325\end{aligned}\)
Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325
During lunch on Friday, 45 students in the 7th
grade chose pizza. This represented 25% of the
seventh-grade class. How many students are in the
entire 7th grade class?
Answers
Answer:
135
Step-by-step explanation:
Round this number to the nearest ten thousand.
84,759
A. 80,000
B. 84,000
C. 85,000
D. 90,000
Answers
Answer:
Step-by-step explanation:
Answer:
80,000 A
Step-by-step explanation:
it is under 85000 so it is rounding down to 80,000
Help Me :^
What is the quotient?
~Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth~
a. Negative 1 and one-half
b. Negative StartFraction 3 over 32 EndFraction
c. StartFraction 3 over 32 EndFraction
d. 1 and one-half
Answers
Answer:
d
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
Answer:
d madam
Step-by-step explanation:
edge 2021