To estimate the fraction of people interested in your new product, you can use the sample proportion. By dividing the number of people interested (sum of x's equal to 1) by the sample size, you can obtain an estimate of the underlying fraction.
The Chebyshev inequality can be used to find a lower bound on the sample size required to ensure a certain level of confidence in the estimate. The Central Limit Theorem (CLT) allows us to approximate the distribution of n(Wn - W) as a normal distribution, where Wn is the sample proportion and W is the true fraction of people interested. By using the CLT, we can determine an approximate lower bound on the sample size required to ensure a desired level of confidence.
a. To estimate the bf people interested in the new product, calculate the sample proportion (Wn) by dividing the sum of x's equal to 1 by the sample size (n). The sample proportion gives an estimate of the underlying fraction of interest.
b. The Chebyshev inequality states that for any random variable with finite variance, the probability that it deviates from its mean by more than k standard deviations is at most 1/k^2. In this case, we want to ensure that P(|W - Wn| < 0.05) > 0.95. By setting k = 0.05/(standard deviation of Wn), we can find the corresponding lower bound on the sample size needed.
c. The CLT states that for a sufficiently large sample size, the distribution of n(Wn - W) approaches a normal distribution with mean 0 and variance (1/4)*(1/n), where Wn is the sample proportion. This approximation allows us to use normal distribution properties to estimate probabilities.
d. By using the CLT approximation, we can find the sample size required to ensure P(|W - Wn| < 0.05) > 0.95. We can use the Z-table or Q-function table to find the corresponding Z-value for the desired level of confidence and calculate the lower bound on the sample size using the formula n ≥ (Z-value * standard deviation of Wn / 0.05)^2.
Learn more about sample size here: brainly.com/question/30100088
#SPJ11
In comparison to where would be
located on a number line?
A.closer to 0
B.the same point
C.closer to 1
D.at 0
y = 3x - 5 and y = 4x.
Answer: x = -5
New Equation (after substituting) 4x = 3x - 5
Subtract 3x from both sides
x = -5
The Bungling Brothers Circus is in town and you are part of the crew that
is setting up its enormous tent. The center pole that holds up the tent
is 70 feet tall. To keep it upright, a support cable needs to be attached to
the top of the pole so that the cable forms a 60° angle with the ground.
a) How long is the cable?
b) How far from the pole should the cable be attached to the ground?
Answer:
a. 80.83 ft b. 40.42 ft
Step-by-step explanation:
Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.
a) How long is the cable?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,
sinФ = h/L
L = h/sinФ
L = 70 ft/sin60°
L = 70 ft/0.8660
L = 80.83 ft
b) How far from the pole should the cable be attached to the ground?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,
tanФ = h/x
x = h/tanФ
x = 70 ft/tan60°
x = 70 ft/1.7321
x = 40.42 ft
The length of the cable is 80.83 ft and the distance from the pole should the cable be attached to the ground is 40.42 ft and this can be determined by using the trigonometric function.
Given :
The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a 60° angle with the ground.a) The trigonometric function can be used in order to determine the length of the cable.
[tex]\rm sin\theta=\dfrac{h }{L}[/tex]
where h is the height of the pole, L is the length of the pole, and [tex]\theta[/tex] is the angle from the ground.
Substitute the known terms in the above expression.
[tex]\rm L=\dfrac{h }{sin\theta}[/tex]
[tex]\rm L = \dfrac{70}{sin60}[/tex]
L = 80.83 ft.
b) The trigonometric function can be used in order to determine the distance from the pole should the cable be attached to the ground.
[tex]\rm tan \alpha =\dfrac{h}{x}[/tex]
where x is the distance between pole and cable.
Substitute the known terms in the above expression.
[tex]\rm x = \dfrac{70}{tan 60 }[/tex]
x = 40.42 ft.
For more information, refer to the link given below:
https://brainly.com/question/21286835
i need help the test is time and i have 5 min left can y'all pls help pls
Answer:
divide the figure into two parts.
area of square = side²
area of square =12²
area of square =144
area pf trapezium =1/2×(a+b)×h
area of trapezium =1/2×(12+6)×12
area of trapezium =108
area of polygon=144+108=252 unit²
Ilsa withdraws $300 from an account that had a balance of $1,000. How much interest will she earn on the remaining balance at a simple annual interest rate of 1.8% over 3 years?
Answer:
37.8
Step-by-step explanation:
1000 - 300 = 700
I = Prt
I = (700)(1.8%)(3)
I = 37.8
The radius of a baseball is about 9.25 inches. The radius of the Basketball is 9.55 inches. What is the
difference of the volumes between the basketball and baseball?
331.55
2734.89
333.14
364.52
Answer:
C. 333.14
Step-by-step explanation:
Both the basketball and baseball has got the shape of a sphere. So that;
volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius
i. Volume of the baseball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.25)^{3}[/tex]
= 3315.5655
volume of the baseball = 3316.57 cube inches
ii. Volume of the basketball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.55)^{3}[/tex]
= 3649.8372
Volume of the basketball = 3649.84 cube inches
The required difference = volume of basketball - volume of baseball
= 3649.84 - 3316.57
= 333.27 cube inches
The difference of the volumes of the basketball and baseball is 333.27 cube inches.
Pls help, question on picture, will do brainliest if right
no links!!!!!
Answer:
12/13
Step-by-step explanation:
side² = 13² - 5² = 169 - 25 = 144
side = √144 = 12
sin ∅ = 12/13
Their 47 students need a seat on the school bus. If there are 21 student seats on a school bus. How many school buses will need to let each student have a seat?
Answer: 3 buses
Step-by-step explanation:
Answer:
Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.
Step-by-step explanation:
f ( x ) = − x 2 − 12 Find f ( − 3 )
Answer:
f(-3)=-21
Step-by-step explanation:
f(x)=-x2-12
f(-3)=-(-3)2-12
f(-3)=-9-12
f(-3)=-21
Answer:
-3
Step-by-step explanation:
x=-3 substitute in the equation
+3 squared-12=-3
Fill in the blank: Let l be the line of equation (x,y)=(2,1)+t(4.3) And let Q=(-28,41) be a point in the plane. The distance from point Q to the line is:____________
To find the distance from point Q=(-28, 41) to the line represented by the equation (x, y) = (2, 1) + t(4, 3), we can use the formula for the distance between a point and a line in the coordinate plane. Therefore, the distance from point Q to the line is 233/5.
The distance between a point (x0, y0) and a line Ax + By + C = 0 is given by the formula:
d = |Ax0 + By0 + C| / √(A^2 + B^2)
In this case, we have the line represented parametrically as (x, y) = (2, 1) + t(4, 3), where t is a parameter. To use the formula, we need to convert this parametric representation to the standard form Ax + By + C = 0.
Expanding the parametric equation, we have:
x = 2 + 4t
y = 1 + 3t
From these equations, we can rearrange them to isolate t:
t = (x - 2) / 4
t = (y - 1) / 3
Setting the two expressions for t equal to each other, we get:
(x - 2) / 4 = (y - 1) / 3
Simplifying, we have:
3x - 6 = 4y - 4
4y - 3x = 2
Now we have the equation of the line in standard form. The coefficients A, B, and C are 4, -3, and 2, respectively.
To find the distance between point Q=(-28, 41) and the line, we can substitute the values into the distance formula:
d = |4(-28) + (-3)(41) + 2| / √(4^2 + (-3)^2)
Calculating the numerator and the denominator, we have:
d = |-112 - 123 + 2| / √(16 + 9)
d = |-233| / √25
d = 233 / 5
Therefore, the distance from point Q to the line is 233/5.
Learn more about parametric equation here:
https://brainly.com/question/30748687
#SPJ11
2. Two points are shown on the coordinate plane. How any units apart are
Point A and Point B?*
Answer:
Step-by-step explanation:
vocab word for this definetion
Answer:
whats the definition?
Step-by-step explanation:
the solution of the equation (x+3)2=7 is
Answer:
x=1/2
Step-by-step explanation:
A hot air balloon pilot begins to land her balloon. In the first minute the balloon's elevation -336 feet. In the second minute, the balloon's elevation changes by 1/16 of that amount. What is the balloon's elevation during the second minute?
Answer:
-21 Feet
Step-by-step explanation:
-336/16
The balloon's elevation during the second minute will be 21 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.
Then the balloon's elevation during the second minute is given as,
⇒ - 336 x (1/16)
⇒ - 336 / 16
⇒ - 21 feet
The balloon's elevation during the second minute will be 21 feet.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
in the one-way anova f test for comparing several means, the alternative hypothesis states that group of answer choicesthe population means are not all equalthe sample means are not all equalthe sample means are all differentthe sample means are all equalthe population means are all differentthe population means are all equal
The alternative hypothesis in the one-way ANOVA F test states that the population means are not all equal.
In the one-way ANOVA F test, we are comparing the means of several groups or categories. The null hypothesis assumes that all population means are equal, while the alternative hypothesis suggests that there is a difference between at least two of the population means.
The alternative hypothesis can be stated as "the population means are not all equal," indicating that there is variability or disparity among the different groups being compared.
By rejecting the null hypothesis and accepting the alternative hypothesis in the one-way ANOVA F test, we conclude that there is evidence to suggest that the means of the different groups are not equal, indicating some form of group differentiation or distinction in the underlying populations.
To learn more about one-way ANOVA, click here: brainly.com/question/29752518
#SPJ11
Solve system of equations given below using both inverse matrix (if possible) and reduced row echelon forms. (20 Points each) a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7 - b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0.
The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.
a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7
We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.
We begin by converting the above equations into matrix form as follows:
[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]
We represent the coefficient matrix by A and the variable matrix by X.
Then we have AX = B where B = [1] [-3] [7]
To find the inverse of A.
If the inverse of A exists, we can use it to find X = A^(-1)B.
We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.
We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]
Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]
We can use A^(-1) to find X as follows:
X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]
Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.
We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]
The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.
The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:
x + (3/2)z = (-1/2)y + (1/7)z = (4/7)
Solving for z, we have: z = 2/3
Substituting z into the first equation, we have:
x + (3/2)(2/3) = (-1/2)x = -5/3
Substituting z into the second equation, we have:
y + (1/7)(2/3) = (4/7)y = 1/3
Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0
To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]
We represent the coefficient matrix by A and the variable matrix by X.
Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].
We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]
The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.
The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:
x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4
Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.
To learn more about matrix
https://brainly.com/question/28180105
#SPJ11
Suppose the longest side in a right triangle has the measure 4,6. If the acute angles have the measure of 30° and 60°, which is the exact measure of the longer leg?
PLEASE ACCTUALY HELP :<
Point A has the coordinates (-2,-4). Point A is reflected across the x-axis to create point 'A'. What are the coordinates of point "A"? Enter your answer in the space below.
Answer:
(-2, 4)
Step-by-step explanation:
Hopes this helps!
What did the girl mushroom say about the boy mushroom after their first date
Answer:
what’d she say? xD
Step-by-step explanation:
The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.
What is mushrooms?A mushroom is the reproductive structure produced by some fungi. It is somewhat like the fruit of a plant, except that the "seeds" it produces are in fact millions of microscopic spores that form in the gills or pores underneath the mushroom's cap.
here, we have,
She said that he was a fun gi.
This is a pun because fungi is a mushroom and here it is a play on words because of "fun guy" sounding the same as "fun gi".
Since they are both mushrooms, the joke stands and these types of puns are very common among people because of their simplicity.
The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.
To learn more on mushroom click:
https://brainly.com/question/4123628
#SPJ2
Consider the following system of linear equations given by:
3,5x12 +23 3x1 +102 +53 3x1+3x2+7, 25x3 0: = 4; (1)
(a) Verify that the system described by Eq. (1) admits a unique solution.
(b) Determine the solution using Gaussian elimination.
(c) Determine an approximation to the solution, with 3 iterations x
(5), using the Methods of
Gauss-Jacobi and Gauss-Seidel with x(0) = [x1(0)1, x2(0), x3(0)]>= [d1, d2, d3]>, where d1 is the first digit of your code. person, d2 is the second digit of your code. of person and d3 is the third digit of your code. of person.
(d) What is the maximum error made in each of the methods? Use the estimate calculation of the
error (absolute or relative) to compose the analysis.
(e) Analyze the results found in (b) and (c), commenting on the differences.
(f) What strategy would you recommend to reduce the maximum error obtained? Justify the recommendation.
(g) Considering the results found, which method do you consider more efficient in solving of the problem?
The system of linear equations admits an unique solution.
The system of linear equations given by:
-x + 3y = 7 ------------------------(1)
2x + y = 4 ------------------------(2)
We can find whether the system of linear equations admits a unique solution or not by using any one of the methods such as elimination, substitution or matrices.
For this question, we can solve the given system of equations using the substitution method:
From Eq. (2), we get:
y = 4 - 2x ------------------------(3)
Substituting Eq. (3) into Eq. (1), we get:
-x + 3(4 - 2x) = 7
=> -x + 12 - 6x = 7
=> -7x = -5
=> x = 5/7
Substituting the value of x in Eq. (3), we get:
y = 4 - 2(5/7)
=> y = 18/7
Therefore, the unique solution of the given system of linear equations is:x = 5/7 and y = 18/7.
Thus, the given system of linear equations admits a unique solution.
#SPJ11
Let us know more about system of linear equations: https://brainly.com/question/21292369.
Is the graph shown below that of a function?
Answer:
yes
Step-by-step explanation:
(-4,9);m=-1/2
Write the equation in point slope form
Answer: y-9=-1/2 x (x+4)
Step-by-step explanation:
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
Answer: Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475
pls help and show work i am so screwed if i don’t do well on this
Answer:
see in the picture mark brainliest if correct
100 POINTSSS PLZZZZZZZZZZZ
Answer:
The correct anser is B. (i think. sorry if wrong) have a wonderfull day. dont let them bring you down. your amazing just the way you are.
Step-by-step explanation:
Step-by-step explanation:
\blue{\large \rightarrow }\: \boxed{ \sf{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }}
Find the probability a randomly selected z-score is between -1 and 1.2. 0.7781 None of these 0.7019 0.7761 0.7263
To find the probability a randomly selected z-score is between -1 and 1.2, we need to use the standard normal distribution table.
A standard normal distribution table shows the area to the left of the z-score. To find the area between two z-scores, we need to find the area to the left of the larger z-score and subtract the area to the left of the smaller z-score. So, the probability that a randomly selected z-score is between -1 and 1.2 is given by: P(-1 ≤ z ≤ 1.2) = P(z ≤ 1.2) - P(z ≤ -1)
Using the standard normal distribution table, we get: P(-1 ≤ z ≤ 1.2) = 0.8849 - 0.1587 = 0.7262. Therefore, the probability that a randomly selected z-score is between -1 and 1.2 is approximately 0.7263, which is the closest option to our answer. The correct option is option D.
To know more about probability refer to:
https://brainly.com/question/27342429
#SPJ11
Recall that a cycle in an undirected graph is a sequence of distinct vertices (V1, V2, ..., Vk) with k > 3 such that the edges {V1, V2}, {V2, V3},..., {Uk-1, Vk} and also {Uk, v1} all exist. (a) Design an algorithm which given an undirected connected graph determines whether the graph has a cycle. If the graph has |V| vertices and |E| edges, your algorithm should run in O([V] + El) time. (b) Justify the correctness and run-time of your algorithm.
The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).
a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.
The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.
Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)
1. Mark u as visited.
2. For every unvisited neighbor v of u, doDFS(v)
3. If v is already on the current path, return true to denote the existence of a cycle.
4. If there is no cycle, return false to denote that the graph does not contain a cycle.
The overall runtime of the algorithm is O(|V|+|E|).
The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.
Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.
Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.
Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
Therefore, the algorithm has a total runtime of O(|V|+|E|).
Know more about Algorithm here,
https://brainly.com/question/28724722
#SPJ11
if f(x) = x^2 which equation represents function g?
OA g(x) = f(2x)
OB. g(x) = f(4x)
Oc. g(x) = 2f(x)
OD. g(x) = f(1/2x)
Answer:
if f(x) = x^2 which equation represents function g?
Step-by-step explanation:
maby ( C) am not sure
The equation represents the function is g(x) = 3f(x).
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We have,
Function, f(x) = x²
The function g(x) is compressed horizontally by a factor of 3, to get the function g(x)
g(x) = kf(x)
Where k = 3.
So, we have:
g(x) = 3f(x)
Learn more about function transformation here:
brainly.com/question/4025726
#SPJ2
Which is missing from step 4?
Add the data for each interval.
Put a point on each line of the y-axis that has data.
Put the data in order in the table.
Create the bars.
Answer:
The answer u put in the thing is correct!
Step-by-step explanation:
An electrical firm manufactures light bulbs that have a lifetime that 15 approximately normally distnbuted with a mean of 850 hours and a standard deviation of 44 hours. Test the hypothesis that 850 hours against the alternative.
Answer : The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.
Explanation:
Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.
Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.
Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours. Mathematically, it is expressed asH0: μ = 850
Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours. Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850. We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation
Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.
Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.
Learn more about Null and alternative hypothesis here https://brainly.com/question/30535681
#SPJ11