Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean.
a. [52.78,64.22]
b. [53.78,63.22]
c. [53.18,63.81]
d. [54.04,62.96]
Answer:
Option a. [52.78,64.22]
Step-by-step explanation:
We are given that a random sample of size 18 is drawn from a population that is normally distributed.
Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5
The pivotal quantity for calculating 95% confidence interval is;
[tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
So, 95% confidence interval about population mean is given by;
P(-2.110 < [tex]t_1_7[/tex] < 2.110) = 0.95
P(-2.110 < [tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.110) = 0.95
P(-2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]{Xbar - \mu}[/tex] < 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
P(X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]\mu[/tex] < X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
95% confidence interval about [tex]\mu[/tex] = [ X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] , X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ]
= [ 58.5 - 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] , 58.5 + 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] ]
= [ 52.78 , 64.22 ]
Therefore, 95% confidence interval about population mean is [52.78 , 64.22].
Michelle invests $1000 at a bank offering 3% compounded quarterly. Write an equation to model the growth of the investment.
A) A = 1000(1.03)4t
B) A = 1000(1+.03
4
)t
C) A = 1000(1+.03
4
)4t
D) A = 1000((1.03)
4
)4t
Answer:
C. [tex]1000( \frac{1+.03}{4})^{4t}[/tex]
Step-by-step explanation:
A rectangle floor is 24 feet long and 9 feet wide. what is it’s area of the floor in square yards?
Final answer:
The area of a rectangle floor that is 24 feet long and 9 feet wide is 216 square feet, which is equivalent to 24 square yards when converted using the fact that there are 9 square feet in a square yard.
Explanation:
The student is asking about the area of a rectangle when the dimensions are given in feet and the answer is required in square yards. To convert the area from square feet to square yards, we need to know the conversion factor between these two units of measurement.
It's established that 1 square yard is equal to 9 square feet. Thus, the area of the floor in square feet is calculated by multiplying the length by the width:
Area in square feet = Length in feet × Width in feet
= 24 ft × 9 ft
= 216 square feet
Next, we convert the area into square yards by dividing by 9:
Area in square yards = Area in square feet ÷ Conversion factor
= 216 sq ft ÷ 9 (sq ft/sq yd)
= 24 square yards
Therefore, the area of the floor in square yards is 24 square yards.
Simplify radical expression. Leave in radical form. the squarefoot of 7(the squarefoot of 14+the squarefoot 3)
State the domain of the relation
what is the volume of the cube shown below? 2 1/4
The volume of the given cube is 11.4 cubic units.
What is volume of cube?The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.
The edge of the given cube is [tex]2\frac{1}{4}[/tex] =2.25 units.
We know that, the volume of a cube is a³, where a is an edge.
Here, volume = (2.25)³
= 11.390625
≈ 11.4 cubic units
Therefore, the volume of the given cube is 11.4 cubic units.
Learn more about the volume of a cube here:
https://brainly.com/question/11168779.
#SPJ3
99 POINTS!!!: if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then
what is the central angle,
what is the measure of the arc that 2 pieces together would intercept,
and the equation that represents
and circumference?
PLEASE HURRY!!!
the function f(x)=2^x. the function f(x)= 2^x+k and K < 0. which of the following statements is true
Linda bought circular table clothe that was a radius of 3 feet. What is the circmference to the nearest foot of linda's table cloth? (using Pie 3.14
8.
Howmet Corporation needs $200,000 in 5 years.
Find the required quarterly payment into a sinking fund if funds are invested in an account earning 10% per year compounded quarterly.
$38,050.00
$6,716.00
$32,760.00
$7,830.00
A taco stand sells tacos for $3.25 each. The stands expenses for the day are $210. Define your variables and write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then slice the inequality. Provide your conclusion as a complete sentence.
Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 4, f '(0) = 18
Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
Substituting in f'(0)=18, we get C=18.So, f'(x) = -2x + 12x² - 4x³ + 18.If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
Substituting in f(0) = 4, we get C=4.So, f(x) = -x⁴ + 4x³ - x² + 18x + 4To find the function f, we need to integrate its second derivative, then use the given initial conditions to solve for the constant of integration and find the exact function f(x).
Explanation:To find the function f, we need to integrate its second derivative. We integrate each term of the second derivative separately, using the power rule for integration. So, f''(x) = -2 + 24x - 12[tex]x^2[/tex] becomes f'(x) = -2x + 12[tex]x^2[/tex] - 4[tex]x^3[/tex] + C, where C is the constant of integration. Then, we integrate f'(x) to find f(x), again using the power rule for integration. Finally, we use the given initial conditions, f(0) = 4 and f'(0) = 18, to solve for the constant of integration and find the exact function f(x).
Learn more about Integration here:https://brainly.com/question/31744185
#SPJ2
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk 2 quarts of orange juice 16 cups of milk 32 oz of lemonade . how many gallons of beverages did he buy
The amount of beverages did he buy will be 2 gallons.
What is conversion?Conversion means to convert the same thing into different units.
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk, 2 quarts of orange juice, 16 cups of milk, and 32 oz of lemonade.
We know the conversion
1 pint = 0.125 gallons
1 quart = 0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
Then the amount of beverages did he buy will be
Milk bought
0.125 x 2 = 0.25 gallons
Orange juice bought:
0.25 x 2 = 0.5 gallons
Milk bought:
16 x 0.0625 = 1 gallon
Lemonade bought:
32 x 0.0078125 = 0.25 gallons
Thus total gallons made will be
→ 0.25 + 1 + 0.5 + 0.25
→ 2 gallons
More about the conversion link is given below.
https://brainly.com/question/9414705
#SPJ2
The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 meters. One penguin swims half way around the island before hopping out.
How far did the penguin swim?
Answer:
10pi
Step-by-step explanation:
The answer is 10pi
6(z+2)-2(2z+5)=18 show step by step
A store manager set up a cardboard display to advertise a new brand of perfume. The display is a square pyramid whose base is 18 inches on each side.The height of each triangular face of the pyramid is 12 inches. How much card word was used to make the display?
A. 516 B.756
C.612 D.1080
D is not the answer I tried the teacher marked it wrong
The surface area of the cardboard display is the sum of the area of the square base and the four triangular faces, totaling 756 square inches. This corresponds to answer B.
The student wishes to calculate he amount of cardboard used to create a square pyramid display. To find this, we need to determine the surface area of the pyramid, which includes the base and the four triangular faces.
Firstly, we calculate the area of the square base. The base length is given as 18 inches. The formula for the area of a square is side length squared:
Base area = 18 inches × 18 inches = 324 square inches.Next, we find the area of one triangular face using the formula for the area of a triangle (base × height / 2). The base of each triangle is the same as the side of the square base, and the height is given as 12 inches:
Triangular face area = (18 inches × 12 inches) / 2 = 108 square inches.Since there are four identical triangular faces, we multiply the area of one triangle by four:
Total area of triangular faces = 4 × 108 square inches = 432 square inches.Finally, we add the area of the base to the total area of the triangular faces:
Total surface area = 324 square inches (base area) + 432 square inches (triangular faces area) = 756 square inches.Therefore, the amount of cardboard used for the pyramid display is 756 square inches, which corresponds to answer B.
) 20% of computer chips from a certain manufacturer are defective. if 100 computer chips are purchased, what is the approximate probability that at least 20 of them are defective
PLZ HELP ASAP CIRCLES
The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
Answer:
8
Step-by-step explanation:
I just took the test.
PLEASE HELP -Given the graph of rectangle QUAD and its reflection.
Use the coordinates of the images' vertices, Q and Q' to algebraically find the line of reflection. In your final answer, include all of your work.
Answer:
Q = (-5, 2)
Q' = (6, 2)
(-5 + 6/2 , 2 + 2/2) = (1/2, 2)
Vertical line through the mid point would be x = 1/2
Identify the coefficient of each term of the polynomial.
-2x+9
what is The coefficient of the first term is ....
what isThe coefficient of the second term is
Final answer:
The coefficient of the first term '-2x' in the polynomial is -2, and the coefficient of the second term '9' is 9.
Explanation:
In the polynomial -2x+9, each term has a coefficient. A coefficient is a number that multiplies the variable. The variable in the first term is x, and it is being multiplied by -2. Therefore, the coefficient of the first term is -2. The second term is a constant and does not have a variable associated with it. However, by convention, we can think of this term as 9 times x0, since any number raised to the zero power is 1. The coefficient of this constant term is 9.
Based on the family the graph below belongs to, which equation could represent the graph
Answer: Second option y=log(2x)+3
Solution:
Based on the family of graphs shown in the attached file, the equation could represent the graph is y=log(2x)+3
This graph is the graph of the funtion y=log(x) stretched horizontally by a factor of 2 and translated 3 units upward.
Leo, Kush and Mai share some money in the ratio 3:5:8
Kush receives £750 more than Leo.
Calculate total amount of money that they shared.
Find the nth term of the sequence, then find the 20th term, 100th term and the series for each?
2/5, 1/15, -4/15,....
A surveyor wants to measure the distance from the north end (point b ) to the south end (point c) of a body of water. He creates a right triangle by using point A which is 17.5 m due west of point c and at a 30 degree angle with point b. Find the distance across the lake
The distance across the body of water from point b (north end) to point c (south end) can be found using trigonometry and the sine ratio. Given that the angle is 30° and the distance from point A to point b is 17.5 m, the distance across the water (from point b to point c) is 8.75m.
Explanation:The problem at hand is a trigonometry problem which can be solved by using the sine ratio. In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle is given as 30°, and we are asked to find the distance from point b (north end) to point c (south end), which is the side opposite to the 30° angle. Therefore, we can set up the following equation using the sine ratio: sin(30°) = opposite/hypotenuse.
In this instance, the hypotenuse is the distance from point A to point b, which is given as 17.5 m. Thus, the equation becomes sin(30°) = distance from point b to point c / 17.5 m. Solving this for the distance from point b to point c would mean multiplying both sides by 17.5 m, giving us: distance from point b to point c = sin(30°) * 17.5 m.
Upon calculation, we find that sin(30°) equals 0.5, so therefore the distance from point b to point c, which is the distance across the body of water is 0.5 * 17.5m = 8.75 m.
Learn more about Trigonometry here:https://brainly.com/question/11016599
#SPJ12
Which expression represents the volume of the box? use the formula v=lwh 3x+1, 2x-1 ×+2
One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:the answer is 236 students
Step-by-step explanation:
What do you notice about the median and mean?
Which is the equation of an ellipse centered at the origin with foci on x-axis, x-intercepts +7, -7 and y-intercepts +2,
-2?
Answer:
It's B on edge.
Step-by-step explanation:
the temperature at 10 am was -7°F. By noon, the temperature had dropped 12°F. By 2 pm, it had dropped another 5°F. what was the temperature at 2 pm?