By using the concept of confidence interval, it can be concluded that-
To reduce confidence interval, it is needed to increase sample size.
Option c is correct
What is confidence interval?
Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.
Formula for percentage confidence interval
[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]
We have to reduce the size of the confidence interval
Confidence interval has no effect on mean, directly proportional to standard deviation and inversely proportional to sample size
So to reduce confidence interval, it is needed to increase sample size.
Option c is correct
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Complete Question
After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
Select one:
a. increase the population standard deviation
b. increase the level of confidence
c. increase the sample size
d. increase the sample mean
e. none of these would help
Given the following probability distributions:
Distribution A Distribution B x p(x) x p(x)
0 .50 0 0.05
1 .20 1 0.10
2 .15 2 0.15
3 .10 3 0.20
4 .05 4 0.50
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.
Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).
a) Expected value for the distributions A and B is calculated as follows,
The expected value for distribution A,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]
The expected value for distribution B,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]
b) The standard deviation for the distributions A and B is calculated as follows,
First, find E(X²) for distribution A and B to substitute in the standard deviation formula.
The E(X²) for distribution A is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]
The E(X²) for distribution B is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]
Then, the standard deviation for distribution A is,
[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]
The standard deviation for distribution B is,
[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]
Distribution A and B have the same standard deviation.
c) The standard deviation values are the same for both distributions. But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.
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A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
The change in rate of length of shadow is 2.692 ft/sec.
Given,
Height of tall person =7 ft
Height of tall lamp post = 20 ft
Rate at which tall person walks = 5 ft/sec
Let,
Distance between tall person and lamp post be x ft
the length of shadow be y ft
From similar triangles,
[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]
Differentiating on both sides with respect to time 't'
[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]
here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec
[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]
Thus, the change in rate of length of shadow is 2.692 ft/sec.
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Find the tenth term of the
sequence.
4, 3, 0, -5, - 12, ...
Answer:
-76
each term is being subtracted from the preceding the next odd number
Olaf has 11 more than triple the amount of customers as when he started selling newspapers. He now has 71
customers. Write an equation that can be used to solve for how many customers Olaf had originally, then solve
your equation to find the answer.
The equation representing the situation is written as
3x + 11 = 71the number of customers Olaf had originally is 80
How to write the equationFrom the given information the following is deduced
Olaf has 11 more than triple the amount of customers as when he started selling newspapers
let the amount be x
3x + 11 = ?
He now has 71 customers
3x + 11 = 71
solving the equation
3x = 71 - 11
3x = 60
x = 20
Olaf had 80 customers
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Solve the system algebraically.
4x+2y=104x+2y=10
x=y+13x=y+13
The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
4x + 2y = 10
x = y + 13
Now,
Since, The system of equations are,
⇒ 4x + 2y = 10 ..(i)
⇒ x = y + 13
⇒ x - y = 13 ..(ii)
Multiply by 2 in equation (ii) and add with (i);
⇒ 2x - 2y + 4x + 2y = 26 + 10
⇒ 6x = 36
⇒ x = 6
And, x - y = 13
⇒ 6 - y = 13
⇒ 6 - 13 = y
⇒ y = - 7
Thus, The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
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Nobody ANSERS MY QUESTONS pleas help me
Answer:
∠RPQ = 105
∠R = 45
Step-by-step explanation:
Question 1
By intersecting chord theorem ? = (175 + 35) / 2
? = (175 + 35) / 2
? = 210 / 2
? = 105
(See image below)
Question 2
By intersecting secant theorem ∠R = (140 - 50)/2
∠R = (140 - 50)/2
∠R = 90/2
∠R = 45
(See image below)
Intersecting chord theorem : Corresponding angle equals sum of corresponding arcs divided by two
Intersecting secant theorem : The inscribed angle equals major arc minus minor arc divided by two
A pyramid has a square base with edges that measure 6 meters, and a slant height of 7. 5 meters. What is its surface area? 270 45 126 102.
The surface area of the given pyramid 126 m².
What do you mean by surface area?
A solid object's surface area is a measurement of the overall space that the object's surface takes up.
According to data in the given question,
We have the given information:
A pyramid has a square base with edges that measure 6 meters, and a slant height of 7.5 meters.
Now, we need to determine the surface area of given pyramid,
The formula for a pyramid's surface area with a square base is:
[tex]SA=b^{2}+2*(bs)[/tex]
Where b is the base length and s is the slant height.
We have the following information for the stated situation,
b= 6 m
s= 7.5 m
Then, we will putting the given values in the above formula,
[tex]SA=b^{2}+2*(bs)[/tex]
[tex]SA=6^{2}+2*(6*7.5)\\SA=36+90\\SA=126m^{2}[/tex]
Therefore, the surface area is 126m².
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what is the rule for multiplying two integers that have the same sign
If multiplying 2 negative integers then it's a positive
If multiplying 2 positive integers it's positive
Answer: I hope this is helpful
Step-by-step explanation:
The proceeding pattern is summarized in the following rule for multiplying integers. Rule for Multiplying Two Integers: TO MULTIPLY INTEGERS WITH THE SAME SIGN, multiply the absolute value of the factors. The product is positive.
given the slope m of a line and a point (x, y) on that line, how can you determine the coordinates of another point on the line?
To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
The equation of the line is written in the slope-intercept form, which is:
y = mx + b, where m represents the slope and b represents the y-intercept.
Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.
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Iris's checking account pays simple interest at 5% per year. She has $185 in
Answer:
Step-by-step explanation:
Answer 3700
what is a general pattern in data
Answer:
rhe general pattern in data is........
Step-by-step explanation:
.....
he fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) use the data to test the hypothesis that the proportion is not 0.04. use ????α
The proportion is not equal to 0.04.
The test statistic
Z = 1.149
What is the random sample?
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
Since the calculated value of Z = 1.149 is less than 1.96 at 5% (0.05) level of significance.
The null hypothesis is accepted
Hence the proportion is not equal to 0.04
Given data a random sample of 300 circuits is tested, revealing 17 defectives.
The proportion of success
P = 17 / 300 = 0.056
Null hypothesis:- H₀ = P ≠0.04
Alternative hypothesis:- H₁ = P =0.04
Q = 1-P = 1-0.04=0.96
Level of significance ∝ =0.05
The test statistic
[tex]z = \frac{p -P}{\sqrt{PQ/n} }[/tex]
now substitute all values, and we get
on calculation, Z = 1.149
Since the calculated value of Z = 1.149 is less than 1.96 at a 5% (0.05) level of significance.
The null hypothesis is accepted.
Hence the proportion is not equal to 0.04.
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Ellis's backyard has a 6.25m by 6.25m patio. She would like to build a 1.5m wide extension around 3 sides of the patio. She will buy 0.25m b 0.25m tiles that come 25 to a package. How many packages does Ellis need to buy to build the extension?
Answer:
21
Step-by-step explanation:
The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.
Then there are two square corners added that each one is 1.5 m by 1.5 m.
Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m
Total added area = 28.125 m² + 4.5 m²
Total added area = 32.625 m²
The area of each tile is:
0.25 m × 0.25 m = 0.0625 m²
A box of tiles has 25 tiles. The total area covered by a box of tiles is:
25 × 0.0625 m² = 1.5625 m²
The number of boxes need is:
32.625 m² / 1.5625 m² = 20.88
Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.
Answer: 21
describe a procedure that could be used to write an equation having the first 7 natural numbers as solutions.
the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Now the simplest way to write an equation is to multiply all the factors.
The zeroes of the equation are 1,2,3,4,5,6,7.
The factors can be written as (x-1)* (x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7).
So the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
Hence, the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
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URGENT PLEASE HELP: Ryan planted flowers in a rectangular garden. The width of the garden is (x-8) feet and the length of the garden is 3 feet longer than the width. Write an expression for the area of the
garden.
An expression for the area of the garden is
(Type an expression using x as the variable.)
Answer:
-8 + 3 + x = x - 5
Step-by-step explanation:
This is because X does not have a value & both 8 & 3 are constants making them computable
6x-4y=18 -x-6y=7 solve
Answer:
Solution = (2, 1.5)
Step-by-step explanation:
Step 1: Solve for y in 6x - 4y = 18
1. 6x - 4y = 18 → -4y = -6x + 18 → y = 1.5x - 4.5
Step 2: Substitute 1.5x - 4.5 for y in -x - 6y = 7
2. -x - 6(1.5x - 4.5) = 7
Step 3: Solve for x
3. -x - 9x + 27 = 7 → -10x + 27 = -20 → -10x = -20 → x = 2
Step 4: Substitute 2 for x in -x - 6y = 7
4. -(2) - 6y = 7
Step 5: Solve for y
5. -2 - 6y = 7 → -6y = 9 → y = -1.5
Hope this helps you out :)
At what point do the curves and intersect? find their angle of intersection correct to the nearest degree.
The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
What are angles?When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.
When two rays are linked at their ends, they create an angle in geometry.
The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.
Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
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he points (12,10) and (30,25) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.
Given that points (12,10) and (30,25) form a proportional relationship.
The slope of the line passing through the two points will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 25-10 ) / ( 30-12 )
Slope = 15 / 18
Slope = 5 / 6
Therefore, the slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
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customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
The probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.
Given that.
The percentage of customers who will disclose a food allergy is 0.08
At Ying Ying's bakery, 121 people place orders on a single day.
We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.
Formula for Binomial probability distribution:
P(X=x)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ
Where P(x)= probability of getting success in x trials,
n= sample size ,
p represents the probability that each event will succeed.
As stated, we have n=12
p=0.08
Let x signify that the client will disclose a food allergy.
Following that, the probability that at least one client will disclose a food allergy will be:
P(x≥1)=1-P(x<1)
=1-P(x=0)
=1-¹²C₀(0.08)⁰(1-0.08)¹²⁻⁰
=1-(1)(0.12)¹²
=1-0.3677
=0.6323
Therefore, the probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.
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1. Write the slope-
intercept form
(y=mx+b) of the line
with a slope of -1/2and
one ordered pair (-6, 4).
a piece of wire 10 m long is cut into two pieces. one piece is bent into an equilateral and the other is bent into a circle. how should the wire be cut so that the total area enclosed is (a) a maximum? (b) a minimum?
For maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
What is the area of any geometrical shape?
The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.
Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.
One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.
Perimeter = 3 m
3*side = 3 m
side = 1 m
Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]
A = 0.4330 m² -----(I)
Now the circumference of the circle = 5 m
2π×r = 5
r = 5/2π
r = 0.7957 m.
Now the area of the circle = π×r²
= 3.14 × (0.7957)²
= 1.988 m² --------(II)
From (I) and (II), we can say that
Area of the equilateral triangle < Area of the circle
Hence, for maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
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A professor wants to estimate how many hours per week her students study. A simple random sample of 65 students had a mean of 16 hours of studying per week. Construct a 98% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.4 hours per week. Round to two decimal places. Answer 2 Points Keypad Keyboard Shortcuts Lower Endpoint Upper Endpoint: Prev
98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
mean x = 16
standard deviation σ = 2.4
sample size n = 65
z score for 98% = 2.576
Interval = x±z*s/
= 16±2.576*2.4/
= 16±2.576*0.39629
= 16±1.0208
Interval = (21.0208,18.9792)
Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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What is the value of x?
Enter your answer in the box.
Answer:
x=36
Step-by-step explanation:
Work in attachment
any of y'all willing to do this? me on gram quietstorm703
read my comments
What is your question dude???????
A recipe for cheesecake requires 3 cups of sugar per
batch.
A. Write an equation that can be used to determine y,
the number of cups of sugar required to make
cheesecake, based on x, the number of batches.
B. Use your equation to determine how many cups of
sugar are required to make 4 batches of cheesecake.
Pls hurry!!
Answer:
y = x × 3, 12
Step-by-step explanation:
If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:
y = x × 3
Using this, we can determine how many cups are needed when we need to make 4 batches.
y = 4 × 3 = 12
You need 12 cups of sugar for 4 batches.
amanda chicopee bought a new car and drove 8,000 miles in the first four months. at the same rate, how many miles will amanda drive in 3 years?
If Amanda stays on her current course, she will go 72,000 km in three years.
Given data,
In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?
Here,
She drove 8000 km in 4 months.
⇒ In 1 month = 8000/4 = 2000 km
To find how many miles in 3 years,
⇒ In 36 months = 2000 * 36
= 72000 km
Hence, 72000 km will Amanda log in three years if she continues on her path.
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10 degrees
below 0
Is it negative or positive or zero
Answer:
Step-by-step explanation:It's -10 degrees
d • r = r • d what is the property
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
Hope it helps!
5/3 x + 1/3 x = 40/3 + 8/3 x
Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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