eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:
Answers
The 90% confidence interval for the class is [73.49, 76.51].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x SD/√n
where CI = confidence interval
μ = sample mean = 75
z = found by using a z-score table
SD = sample standard deviation = 5
n = sample size = 30
At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.65
Plug in the values to the formula for confidence interval, CI.
CI = μ ± z x SD/√n
CI = 75 ± 1.65 x 5/√30
CI = 75 ± 1.51
CI = [73.49, 76.51]
Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.
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Related Questions
an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
Answers
The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
What is probability?
Probability is defined as the possibility of an event to occur.
An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]
Thus probability of success will be [tex]p=0.98[/tex]
So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]
To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.
Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]
Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
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How many solutions does this equation have?
-7k 2k= -9k
no solution
one solution
infinitely many solutions
Submit
Answers
Answer:
1 answer
Step-by-step explanation:
when the terms are collected
[tex]4k = 0[/tex]
[tex]k = 0[/tex]
Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Answers
Graph 1 contains the two angles in the domain 0 ≤ θ ≤ 360º that have cosine given by cos(θ) = -3/5.
Where is the cosine of angle negative?The sine and the cosine of an angle are represented in the unit circle, in which:
The x-axis is composed by the cosine of the angle.The y-axis is composed by the sine of the angle.Hence the cosine of the angle is negative when the x-axis is negative, which happens in these following quadrants:
Second quadrant.Third quadrant.The only equation that can be solved in the context of this problem is:
cos(θ) = -3/5.
The solution is composed by two angles, one in the second quadrant and one in the third quadrant, hence Graph 1 shows the correct solution.
The exact angles are found applying the inverse cosine function as follows:
θ = arccos(-3/5) = 126.9º = 233.1º.
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Find the value of x that satisfies the given conditions. Then graph the line on a separate sheet of paper.
The line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2, -9) and (3,-4).
Answers
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The condition is;
The line containing the points (4, -2) and (x,-6) is perpendicular to the line containing the points (-2, -9) and (3,-4).
Since, Multiplication of Slopes of perpendicular lines are -1.
That is;
m₁ m₂ = -1
Where, m₁ is slope of first perpendicular line and m₂ is slope of second perpendicular line.
Now, Find the slopes of lines as;
m₁ = (-6 - (-2)) / (x - 4)
m₁ = - 6 + 2 / x - 4
m₁ = - 4 / (x - 4)
And, Slope of second line,
m₂ = (-4 - (-9)) / (3 - (-2))
m₂ = (-4 + 9) / (3 + 2)
m₂ = 5 / 5
m₂ = 1
Hence,
m₁ m₂ = -1
Substitute all the values, we get;
- 4 / (x - 4) × 1 = -1
4 = x - 4
x = 4 + 4
x = 8
Thus, The points on the line is (4 , -2) and (8 , -6).
So, Slope (m₁) = (- 6 - (-2)) / (8 - 4)
= (-6 + 2) / 4
= - 4 / 4
= -1
Thus, The equation of line passing through the points (4 , -2) and
(8 , -6) with slope -1 is;
y - (-2) = - 1 (x - 4)
y + 2 = -x + 4
y = - x + 4 - 2
y = - x + 2
Therefore,
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
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Can someone tell me what x and y is and how to solve for it
Answers
[tex]2x = 76[/tex]
Due to alternate angles
[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]
40°+(y-8)°+76°=180°(sum of angles in a triangle)
[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]
ATTACHED IS THE SOLUTION.
Answer:
x = 38 ; y = 72
Step-by-step explanation:
180 = 76 + 40 + (y - 8)
180 = 108 + y
72 = y
The triangle has parallel lines, so the uppermost right angle is also 90 degrees.
90 - 76 = 14
180 = 90 + 14 + 2x
180 = 104 + 2x
76 = 2x
38 = x
The store at which Andy usually shops is having a sale. Roast beef cost four dollars a pound and shrimp cost $10 a pound. Write an equation to describe different possible combinations of roast beef and shrimp that he can buy for $96.
Answers
The equation to describe different possible combinations of roast beef and shrimp that he can buy for $96 is 4b + 10s = 96.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let roast beef = b
Let shrimp = s
Total cost = 96
Therefore the equation will be:
(4 × b) + (10 × s) = 96
4b + 10s = 96
This illustrates the equation.
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Solve the equation. -5x + 1 = 31 x=
Answers
we get that:
[tex]\begin{gathered} -5x+1=31\rightarrow-5x=31-1=30 \\ x=-\frac{30}{5}=-6 \end{gathered}[/tex]so the answer is x=-6
joanne graphed a linear funtion with a slope of -4 passing through 0,-2 nick graphed the function y=-2x - 4
Answers
Answer:
Explanation:
The slope-intercept form of the equation of a line can be written as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So if Joanne graphed a linear function with a slope(m) of -4 passing through (0, -2), let's go ahead and determine the y-intercept of the line as shown below;
[tex]\begin{gathered} -2=-4(0)+b \\ -2=b \\ b=-2 \end{gathered}[/tex]Therefore, the equation of line will be y = -4x - 2 as graphed below;
Given Nick's function as y = -2x - 4, combining both graphs, we'll have the below;
The red line is Joanne's line while the blue line is Nick's line.
We can see from the above graph of both lines that Joanne's line intersects the y-axis above Nick's line's
Consider the calculation x - y + (- z) where x and z are positive real numbers and y is a negative real number. i) What are the directions of motion for this calculation ? ii) Is the final answer positive , negative , or undetermined ? i) Right, left , left ii) Undetermined i) Right , right , left ii) Undetermined i) Right , left , left ii) Negative i) Right right , left ii) Positive
Answers
Given
x - y + (- z) where x and z are positive real numbers and y is a negative real number.
Find
i) What are the directions of motion for this calculation ?
ii) Is the final answer positive , negative , or undetermined ?
Explanation
i) as we have given
x - y + (- z)
x - y - z
(x - y) - z
right -left - left
ii) for this we take examples
let x = 2 , y = -1 and z = 2
2- (- 1) + (- 2) = 1 , positive
now
let x = 2 , y = -1 and z = 5
2 - (- 1) + (- 5) = 3 - 5 = -2 , negative
so , it is both negative or positive
hence it is undetermined
Final Answer
Hence , the correct option is
i) Right, left , left
ii) Undetermined
In comparative statistics, what type of error occurs when a test indicates a significant difference between two or more populations even though the null hypothesis is true?.
Answers
Type 1 error is the error occurs when a test indicates a significate difference between two or more populations.
What does a Type I mistake mean?Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.
Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.
Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.
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Justin works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 30% of his total sales for the week. How much would Justin make in a week in which he made $2425 in sales? How much would Justin make in a week if he made x dollars in
Answers
We can convert that 30% into a decimal, as: 0.3 (That's 30/100)
Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.
For example, let's take Justin's commission:
[tex]2425\cdot0.3=727.5[/tex]Adding this to his base salary,
[tex]450+727.5=1177.5[/tex]We can conclude that Justin's paycheck for the week would be $1,117.5
Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:
[tex]0.3x+450[/tex]Which of the following is TRUE for every polynomial P with degree = n ?a) The highest power of x in P(x) is n-1b) There are at most n-1 solutions to P(x) = 0c) The graph of P has at most n-1 turning pointsd) The graph of P has at most n-1 x-intercepts
Answers
We need to identify the true statement for every polynomial P with degree n.
The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial
[tex]x³+3x²+3[/tex]has degree 3, since the highest power of x has exponent 3.
Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.
About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.
As an example, for P(x) = x²+4, we have:
[tex]\begin{gathered} x²+4=0 \\ \\ x²=-4 \\ \\ x=\pm\sqrt{-4} \\ \\ x=\pm2\sqrt{-1} \\ \\ x=\pm2i \\ \\ x_1=-2i \\ \\ x_2=2i \end{gathered}[/tex]The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.
Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.
Therefore, (c) is True.
We can see that (d) is False from the following example:
the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.
Answer:
c) The graph of P has at most n-1 turning points
HELP NEEDED FOR GEOMETRY PROOFS!!! I will give brainliest
Answers
The method used to prove the specified geometric relationship between the angles and sides of the triangles are as follows:
24. ΔDAE ≅ ΔBAC by SAS postulate, therefore
∠B ≅ ∠E CPCTC25. ΔACD ≅ ΔBCD by ASA postulate
∡A ≅ ∡B CPCTC26 ΔACD ≅ ΔBCD LH postulate.
∡A ≅ ∡B CPCTCWhat are the congruency postulates?The congruency postulates include, SSS, Side-Side-Side, AAS, Angle-Angle Side, SAS, Side-Angle-Side, HL, Hypotenuse Leg.
24. The two column proofs are presented as follows;
Statements Reasons
1. [tex]\overline{CD}[/tex] bisects [tex]\overline{BE}[/tex] 1. Given
2. [tex]\overline{BA}[/tex] = [tex]\overline{AE}[/tex] 2. Definition of bisected line
3. . [tex]\overline{BA}[/tex] ≅ [tex]\overline{AE}[/tex] 3.. Definition of congruency
4. [tex]\overline{CA}[/tex] = [tex]\overline{AD}[/tex] 4. Definition of bisection of line [tex]\overline{CD}[/tex]
5. [tex]\overline{CA}[/tex] ≅ [tex]\overline{AD}[/tex] 5. The definition of congruency
6. ∠DAE ≅ ∠BAC 6. Vertical angles theorem
7. ΔDAE ≅ ΔBAC 7. SAS congruency postulate
8. ∠B ≅ ∠E 8. CPCTC
The acronym, CPCTC represents Corresponding Parts of Congruent Triangles are Congruent
25. Statement Reasons
1. [tex]\overline{CD}[/tex] ⊥ [tex]\overline{AB}[/tex] 1. Given
2. [tex]\overline{CD}[/tex] bisects ∠ACB 2. Given
3. ∠3 = ∠4 = 90° 3. Definition of bisected lines
4. ∠1 ≅ ∠2 4. Definition of bisected angle ∡ACB
5. ΔACD ≅ ΔBCD 5. ASA congruency postulate
6. ∡A ≅ ∡B 6. CPCTC
26. Statement Reason
1. m∠1 = m∠2 = 90° 1. Given
2. ΔACD and ΔBCD are right triangles 2. Definition
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex] 3. Given
4. [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] 4. Reflexive property
5. ΔACD ≅ ΔBCD 5. LH Congruency postulate
6 ∡A ≅ ∡B 6. CPCTC
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Select the correct answer.
Consider this function.
f(x) = 2x -2
Which graph represents the inverse of function f?
A. The first graph (Y)
B. The second graph (W)
C.The third graph (X)
D. The last graph (Z)
Answers
Answer:
option
Step-by-step explanation:
THE THIRD GRAPH(X)
4x5y² how would I solve this
Answers
multiply the numbers
Answer is 20y2
HELP PLS Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answers
Answer: [tex]m=\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
Choose two points and insert them for x and y.
(3,0) and (0,-4) will work
If you need extra help ask me, I'd be glad to help but i encourage you to try to solve it yourself
5.45 into a fraction
Answers
Answer:
[tex]\frac{109}{20}[/tex]
Step-by-step explanation:
.45 mean [tex]\frac{45}{100}[/tex] so 5.45 means 5 [tex]\frac{45}{100}[/tex] = [tex]\frac{9}{20}[/tex] If I divide the top and bottom of [tex]\frac{45}{100}[/tex] by 9
5 [tex]\frac{9}{20}[/tex] is a mixed number. I can make this an improper fraction by changing 5 to 1+1+1+1+1 Another name for 1 is any number over itself as a fraction.
I am going to write 1 as [tex]\frac{20}{20}[/tex]
5 can be written
[tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] = [tex]\frac{100}{20}[/tex]
5 [tex]\frac{9}{20}[/tex] Can be written
[tex]\frac{100}{20}[/tex] + [tex]\frac{9}{20}[/tex] = [tex]\frac{109}{20}[/tex]
Answer:
(109/20) Is the answer.
Number One in the photo provided
Answers
a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33
b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15
c. np = 9.68 and nq = 34.32 where n = 44 and p = .22
Solution:a. Given n = 27
p = 0.33
np = 27 x 0.33
= 8.91
nq = 27 x (1 - 0.33)
= 18.09
For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.
Since here np < 10 approximation is not applicable.
μp = np = 27 x 0.33
= 8.91
σp = √npq = √(27)x (.33) x (1 - 0.33)
= 2.443
b. n = 25 and p = 0.15
np = 25 x 0.15
= 3.75
nq = 25 x (1 - 0.15)
= 21.25
Approximation is not possible because np < 10.
c. n = 44 and p = .22
np = 44 x 0.22
= 9.68
nq = 44 x (1 - 0.22)
= 34.32
Since here np< 10 approximation is not possible.
μp = np = 44 x 0.22
= 9.68
σp =√npq = √(44)x (.22) x (1 - 0.22)
= 2.747
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shelly sews a square blanket that has an area of 144 square feet. it has 36 square blocks, each the same size. what is the approximate length of each side of a block? (1 point)
Answers
The side of the square of each block = 2 feet
Given,
Shelly sews a square blanket that has an area of 144 square feet.
and, it has 36 square blocks, each the same size.
To find the approximate length of each side of a block
Now, According to the question:
36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks
= 144/ 36
= 4
The area of each square = 4 square feet
We know that
Area of square = side ^2
Side ^2 = 4
side = [tex]\sqrt{4}[/tex]
Side = 2
Hence, The side of the square of each block = 2 feet
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simplify the expression then write a rule for the pattern (√t)²
Answers
The expression of (√t)² is t.
What are square and square roots?A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value. In the event that 'a' is the square root of 'b,' then a a = b. Any number has two square roots, one with a positive value and the other with a negative value, because any number's square is always a positive number. As an illustration, the square root of 4 has the values 2 and -2. A number's power 1/2 value is represented by a number's square root. In other words.
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Need an explanation why it’s 46.4
Answers
The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.
What is the perimeter of a triangle?The length of a triangle's boundary taken as a whole is referred to as its perimeter.A triangle is a polygon with three sides, and depending on the size of the sides and angles, there are various varieties of triangles.Any 2D shape's perimeter is determined by the total distance encircling it.Since perimeter indicates how long a shape's perimeter is, it is given in linear units.Calculate the perimeter of a triangle:
Perimeter of a triangle = a +b + c
a = 2 *9 = 18b = 2 * 7 = 14c = 2 * 7.2 = 14 .4a +b + c = 18 +14 +14.4 = 46.4Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.
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If the point B (-1, -10) is reflected over the line y = x, the coordinates of B’ would be ________.
Answers
For the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).
As given in the question,
Given points :
B (-1, -10)
Reflected over the line y = x
Reflected represents the transformation which shows the movement of original points to the new location. There are different types of transformation such as reflection, rotation, dilation , and translation.
Reflection represents the flipping of the points over the line y =x.
B(x, y) and B'(y, x).
For the given points B (x, y) = (-1,-10) is reflected over the line y =x , the coordinates of B'(y, x) = ( -10 , -1).
Therefore, for the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).
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Dwayne puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded quarterly. How much will be in the account after 4 years? nt 1 Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting n amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answers
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
P= 200
r= 0.09
n = 4
t= 4
And solving we got:
[tex]A=200(1+\frac{0.09}{4})^{4\cdot4}=285.52[/tex]
Write answer in scientific notation
(1.94 × 10³) (8 × 10")
Answers
Scientific notation the
At basketball practice you made 21 out of 80 shots.
Which choice is closest to the percentage of shots you made?
Answers
Answer: 26.25% basketball practice
Step-by-step explanation: At basketball practice I made 21 out of 80 shots.
Therefore the percentage of shots I made is = 21/80×100%
=26.25%
f(x) = 2x³ - 4x + 6
f(3) =
Answers
Graph the cubic using its end behaviour and a few selected points.
The leading coefficient test requires one variable only
An acorn fell from a branch 20 feet high and landed on a branch 7 feet high. How long did it
take the acorn to fall?
Answers
It will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
What is defined as the speed of object?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.For the given question,
An acorn fell from a branch 20 feet high.
An acorn landed on a branch 7 feet high.
The total distance travelled by and acron is 20 - 7 = 13 feet.
Let the final velocity of an acron is 'v'.
The initial velocity of an acron 'u' is zero.
Using third equation of straight line.
v² = u² + 2gsu = 0g = 9.8 /sec²s = 13 feetPut the values.
v² = 2×9.8×13
v = 15.96 ft/sec
Put the value in first equation of straight line.
v = u + gt
15.96 = 0 + 9.8×t
t = 15.96/9.8
t = 1.62 seconds.
Thus, it will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
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[3] How many solutions does the system of equations have? y = 5x - 6 y = 5x + 2
Answers
The system of equations has no solution when solving with elimination or substitution
so No solution is the answer
checking
y = 5x -6 ------(1)
y =5x +2------(2)
5x +2 = 5x-6
5x -5x = -6 -2
0 =-8
hence there is no solution since all variables are eliminated
Your bus is traveling 60 km/hr on a class trip to a museum that is 90
kilometers from your school. How long will it take to get there?
OA. 1.5 hours
O
B. 2.0 hours
O
O
C. 0.5 hour
D. 1.0 hour
Answers
Answer:
nothing but B2. 0 hours
The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
Speed can be thought of as the rate at which an object covers distance.
i.e.
Speed = distance traveled/time taken
After arranging the equation we get,
Time taken = Distance traveled/Average speed
Here distance traveled by bus = 90 km
The average speed of the bus = 60 km/hr
So total time taken = 90/60 = 1.5 hours
So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
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Five boxes of crackers cost 9 at this rate how much do 20 boxes cost
Answers
Answer:
36
Step-by-step explanation:
Unit price: 9 / 5 = 1.8
20 box price: 1.8 * 20 = 36
