Answer:
D) II and III are both correct.
Step-by-step explanation:
The Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The cost of flowers for a wedding is $698. The 95% of all samples of size is 40 and the confidence interval will be mean cost of flowers at wedding. There is confidence that mean cost of wedding flowers is between $701 to $767.
Consider the given function and the given interval.
f(x) = 8 sin x - 4 sin 2x, [0,pi]
(a) Find the average value f ave of f on the given interval.
(b) Find c such that f ave = f(c).
(a) The average value of f(x) on the closed interval [0, π] is
[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]
(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :
8 sin(c) - 4 sin(2c) = 16/π
8 sin(c) - 8 sin(c) cos(c) = 16/π
sin(c) - sin(c) cos(c) = 2/π
Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution
Answer:
±7 sqrt(2) = x
Step-by-step explanation:
98 - x^2 = 0
Add x^2 to each side
98 =x^2
Take the square root of each side
±sqrt(98) = sqrt(x^2)
±sqrt(49*2) = x
±7 sqrt(2) = x
Answer:
[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]
Step-by-step explanation:
[tex]98-x^2 =0[/tex]
[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]
[tex]98=x^2[/tex]
[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]
[tex]\pm \sqrt{98} =x[/tex]
[tex]\sf Simplify \ radical.[/tex]
[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]
[tex]\pm 7\sqrt{2} =x[/tex]
[tex]\sf Switch \ sides.[/tex]
[tex]x= \pm 7\sqrt{2}[/tex]
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale
Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.
Step-by-step explanation:
We have 4 cubes with side lengths of:
6cm, 8cm, 10cm and 12cm.
Now, some things you need to know:
If we want a scale to be balanced, then the mass in both plates must be the same.
The volume of a cube of side length L is:
V = L^3
And the mass of an object of density D, and volume V is:
M = D*V.
As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.
Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:
Cube of 6cm:
V = (6cm)^3 = 216cm^3
Cube of 8cm:
V = (8cm)^3 = 512cm^3
Cube of 10cm:
V = (10cm)^3 = 1000cm^3
cube of 12cm
V = (12cm)^3 = 1728cm^3
First, if we add the volumes of the first two cubes, we have:
V1 = 216cm^3 + 512cm^3 = 728cm^3
Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm
Then the volume of the 3 smaller cubes together is:
V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.
Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.
a department store regularly sells a pair of pants for $49.95. they are having a sale where clothing 30% off.
after including an 8% sales tax, how much do the pants cost on sale?
A. $30.97
B. $38.96
C. $37.76
D. $32.17
Answer:
C. $37.76
Step-by-step explanation:
30% of $49.95
=30/100×49.95
=$14.99
selling price = 49.95 -14.99
= $34.96
8% sales tax included
=8/100×34.96
=$2.80
new price= 34.96+2.80
=$37.76
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
Please help!! find the circumference of a circle with a diameter of 13 meters
Answer:
C = 2pie(r)
r= d/2= 13/2= 6.5
C = 2*3.14*6.5
C= 41
Step-by-step explanation:
perform the indicated operation (8-15i)(-3 + 2i)
Answer:
[tex] - 24 + 16i + 45i + 15 = 9 + 61i[/tex]
Please help. I’ll mark you as brainliest if correct!
Answer:
x and y can have many values
Step-by-step explanation:
-24x - 12y = -16
Then: 24x + 12y = 16
We know: 6x + 3y = 4
X and Y can have a lot of valoues.
6x + 3y = 4
3 ( 2x + y) = 4
2x + y= 4/3
2x+y= 1.333...
The graph of g(x) is the result of translating the graph of f(x) = (one-half) Superscript x three units to the left. What is the equation of g(x)?
Answer:
[tex]g(x) = 0.5^{(x+3)}[/tex]
Step-by-step explanation:
Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),
the way to translate three units to the left is to change x to x+3. This gives our answer: [tex]g(x) = 0.5^{(x+3)}[/tex]
Answer:
B. g(x) = (1/2)⁽ˣ⁺³⁾
Hope this helps!
Step-by-step explanation:
if the LCM and the HCF of two numbers are 9 and 3, respectively, what are the numbers?
Hey There!
Answer:
HCF = 9 (With the two numbers) - 18,9LCM = 3 (with the two numbers) - 6,9Step-by-step explanation:
HCF
If HCF is ''9'' that means that ''9'' is the divisible of two numbers.
So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.
And always remeber the answer is a ''Prime factor.''
LCM
If LCM is ''3'' that means ''3'' is the lowest common multiple out of two numbers.
Hope this helps!
Have a nice Day!:)
Find the sum. 31.25 + 9.38
Answer:
40.63
Step-by-step explanation:
31.25+9.38= 40.63
Hope this helps
Answer: 40.63
Look at the image for shown work.
Find the side length, b.
Round to the nearest tenth.
Answer:
b ≈ 9.2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )
b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )
Answer:
9.22
Step-by-step explanation:
Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].
In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.
[tex]b = \sqrt{6^{2} +7^{2} }[/tex]
b = 9.22
ΔABC is similar to ΔMNO. The scale factor from ΔMNO to ΔABC is 3∕2 . If the area of ΔMNO is 10 square units, what's the area of ΔABC? Question 12 options: A) 45 square units B) 90 square units C) 22.5 square units D) 15 square units
Answer:
The area of ΔABC= 6.667 square units
Step-by-step explanation:
ΔABC is similar to ΔMNO.
The scale factor from ΔMNO to ΔABC is 3∕2
the area of ΔMNO is 10 square units,
The area of ΔABC/the area of ΔMNO
= 2/3
The area of ΔABC/10= 2/3
The area of ΔABC= 2/3 * 10
The area of ΔABC= 20/3
The area of ΔABC= 6 2/3
The area of ΔABC= 6.667 square units
Answer:
22.5 square units
Step-by-step explanation:
i multiplied 10 by 2 to get 20 and went with the closest answer and got it right.
i dont know how to do math but i guess it worked
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of and a standard deviation of . Complete parts (a) through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than . The probability of a student scoring less than is nothing. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between and . The probability of a student scoring between and is nothing. (Round to four decimal places as needed.) (c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than . The probability of a student scoring more than is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. than 0.05. B. than 0.05. C. The event in part is unusual because its probability is less than 0.05. D. The events in parts are unusual because its probabilities are less than 0.05.
The question is incomplete. Here is the complete question.
In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)
(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.
(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.
(d) Identify any unusual events. Explain your reasoning.
Answer: (a) P(X<18) = 0.2033
(b) P(19.9<X<26.7) = 0.4505
(c) P(X>36.4) = 0.0202
(d) Unusual event: P(X>36.4)
Step-by-step explanation: First, determine the z-score by calculating:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
Then, use z-score table to determine the values.
(a) x = 18
[tex]z = \frac{18-23.3}{6.4}[/tex]
z = -0.83
P(X<18) = P(z< -0.83)
P(X<18) = 0.2033
(b) x=19.9 and x=26.7
[tex]z = \frac{19.9-23.3}{6.4}[/tex]
z = -0.67
[tex]z = \frac{26.7-23.3}{6.4}[/tex]
z = 0.53
P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)
P(19.9<X<26.7) = 0.7019 - 0.2514
P(19.9<X<26.7) = 0.4505
(c) x=36.4
[tex]z = \frac{36.4-23.3}{6.4}[/tex]
z = 2.05
P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)
P(X>36.4) = 1 - 0.9798
P(X>36.4) = 0.0202
(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.
The probability will be:
(a) 0.2038
(b) 0.4046
(c) 0.0203
(d) Event in part (c) is unusual.
According to the question,
[tex]\mu = 23.2[/tex][tex]\sigma = 6.4[/tex]Let,
"X" shows the test scores.(a)
The z-score for X=18 will be:
→ [tex]z = \frac{X- \mu}{\sigma}[/tex]
[tex]= \frac{18-23.3}{6.4}[/tex]
[tex]= -0.828[/tex]
So,
The probability will be:
→ [tex]P(X<18) = P(z < -0.828)[/tex]
[tex]= 0.2038[/tex]
(b)
The z-score for X=19.9 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{19.9-23.3}{6.4}[/tex]
[tex]= -0.531[/tex]
The z-score for X=26.7 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{26.7-23.3}{6.4}[/tex]
[tex]= 0.531[/tex]
So,
The probability will be:
→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]
[tex]= 0.4046[/tex]
(c)
The z-score for X=36.4 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{36.4-23.3}{6.4}[/tex]
[tex]= 2.047[/tex]
So,
The probability will be:
→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]
[tex]= 0.0203[/tex]
(d)
Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.
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Which option is correct and how would one solve for it?
Answer:
2+4+6+8
Step-by-step explanation:
We have the sum of 2n where n runs from 1 to 4
n=1 2(1) = 2
n=2 2(2) = 4
n=3 2(3) = 6
n=4 2(4) = 8
The sum is add
2+4+6+8
What is the probability that a student who has no chores has a curfew ?
Answer:
15/22
Step-by-step explanation:
Of the 66 students who have no chores, 45 have a curfew. So the probability is 45/66 = 15/22.
Please help. I’ll mark you as brainliest if correct! Thank you
Answer:
8 pounds of cheaper candy,
17.5 pounds of expensive candy
Step-by-step explanation:
Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!
x + y = 25.5
[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]
We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:
y = 17.5
Plugging this in, we find that:
x = 8.
Whats 18x^3 divided by 7x?????
A computer store sells new computers for $500 and refurbished computers for
$200. In March, the store sold 20 computers for $6,400, meaning they sold ?
refurbished computers.
Answer:
no of new computers sold : 8
no. of refurbished computer sold : 12
Step-by-step explanation:
Let the no. of new computers sold be x
let the no. of refurbished computers sold be y
Given
In March, the store sold 20 computers
x + y = 20
y = 20-x ----- equation 2
selling price of new computer = $500
selling price of x new computer = 500*x = 500x
selling price of refurbished computer = $200
selling price of y refurbished computer = 200*y = 200y
Total selling price of x new computer and y refurbished computers = 500x+200y
given that
total prioce of computer is $6400
thus
500x+200y = 6400
using y = 20-x from equation 2
500x+200(20-x) = 6400
=> 500x+ 4000 - 200x = 6400
=> 300x = 6400 - 4000 = 2400
=> x = 2400/300 = 8
Thus,
no of new computers sold = 8
no. of refurbished computer sold = 20 -8 = 12
An arithmetic sequence has this recursive formula: (a^1 =8, a^n= a^n-1 -6
A.a^n=8+(n-6)(-1)
B.a^n=8+(n-1)(-6)
C.
Answer:
[tex]a_n = 8 + (n - 1) (-6)[/tex]
Step-by-step explanation:
Given
[tex]a_1 = 8[/tex]
Recursive: [tex]a_{n} = a_{n-1} - 6[/tex]
Required
Determine the formula
Substitute 2 for n to determine [tex]a_2[/tex]
[tex]a_{2} = a_{2-1} - 6[/tex]
[tex]a_{2} = a_{1} - 6[/tex]
Substitute [tex]a_1 = 8[/tex]
[tex]a_2 = 8 - 6[/tex]
[tex]a_2 = 2[/tex]
Next is to determine the common difference, d;
[tex]d = a_2 - a_1[/tex]
[tex]d = 2 - 8[/tex]
[tex]d = -6[/tex]
The nth term of an arithmetic sequence is calculated as
[tex]a_n = a_1 + (n - 1)d[/tex]
Substitute [tex]a_1 = 8[/tex] and [tex]d = -6[/tex]
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = 8 + (n - 1) (-6)[/tex]
Hence, the nth term of the sequence can be calculated using[tex]a_n = 8 + (n - 1) (-6)[/tex]
Match each function name with its equation.
Answer:
a. Quadratic--[tex]y=x^{2}[/tex]
b. Absolute Value--[tex]y=|x|[/tex]
c. Linear--[tex]y=x[/tex]
d. Reciprocal Squared--[tex]y=\frac{1}{x^{2} }[/tex]
e. Cubic--[tex]y=x^{3}[/tex]
f. Square Root--[tex]y=\sqrt{x}[/tex]
g. Reciprocal--[tex]y=\frac{1}{x}[/tex]
h. Cube root--[tex]y=\sqrt[3]{x}[/tex]
Answer:
Step-by-step explanation:
y=[tex]x^{2}[/tex] is quadratic
y=x is an absolute value
y= |x| os linear
y= [tex]\frac{1}{x}[/tex] is reciprocal
y= [tex]x^{3}[/tex] is cubic
y= [tex]\sqrt{x}[/tex] is square root
y= [tex]\frac{1}{x^{2} }[/tex] is reciprocal squared
y= [tex]\sqrt[3]{x}[/tex] is cube root
What is the slope of the line shown below?
A. -13/6
B. 6/13
C. 13/6
D. -6/13
-
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
I need help please help meee I don’t understand
Answer:
204
Step-by-step explanation:
To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.
For height of the prongs, take 4 from 6.
6 - 4 = 2
Divide by 2 as there are 2 prongs.
2 / 2 = 1
Remember L * W * H
6 * 3 * 1 = 18
Remember that there are two prongs!
3 + 4 = 7
6 * 7 * 4 = 168
168 + 2(18) = 204
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
In parallelogram PQSR, what is PQ? 2 cm 5 cm 6 cm 9 cm
Answer:
D) 9 cm
Step-by-step explanation:
EDGE 2020
(D) 9 cm.
Parallelogram:A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposed sides and opposite angles because both conditions are a direct result of this postulate.In contrast, a quadrilateral with only one set of parallel sides is referred to as a trapezoid or trapezium in British or American English.The parallelepiped is a parallelogram's three-dimensional equivalent.Therefore, the correct answer is (D) 9 cm.
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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
21, 14, 13, 24, 17, 22, 25, 12
Required:
a. Calculate the sample mean and the sample standard deviation.
b. Construct the 90% confidence interval for the population mean.
c. Construct the 95% confidence interval for the population mean
Answer:
a
[tex]\= x = 18.5[/tex] , [tex]\sigma = 5.15[/tex]
b
[tex]15.505 < \mu < 21.495[/tex]
c
[tex]14.93 < \mu < 22.069[/tex]
Step-by-step explanation:
From the question we are are told that
The sample data is 21, 14, 13, 24, 17, 22, 25, 12
The sample size is n = 8
Generally the ample mean is evaluated as
[tex]\= x = \frac{\sum x }{n}[/tex]
[tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]
[tex]\= x = 18.5[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]
[tex]\sigma = 5.15[/tex]
considering part b
Given that the confidence level is 90% then the significance level is evaluated as
[tex]\alpha = 100-90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 2.995[/tex]
The 90% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]
[tex]15.505 < \mu < 21.495[/tex]
considering part c
Given that the confidence level is 95% then the significance level is evaluated as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 3.569[/tex]
The 95% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]
[tex]14.93 < \mu < 22.069[/tex]
