Answer:
A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.
Step-by-step explanation:
For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...
g(x) = k·f(x)
For translation up by k units, f(x) is transformed to ...
g(x) = f(x) +k
___
Comparing the following ...
f(x) = log(x)
g(x) = 2·log(x) +6
We see that a multiplication factor and an addition factor have been applied. That means ...
g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.
Answer:
A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.
Step-by-step explanation:
For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...
g(x) = k·f(x)
For translation up by k units, f(x) is transformed to ...
g(x) = f(x) +k
___
Comparing the following ...
f(x) = log(x)
g(x) = 2·log(x) +6
We see that a multiplication factor and an addition factor have been applied. That means ...
g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.
Step-by-step explanation:
I just used this and I got it correct
When would you need to arrange polynomials
What is the slope of the line represented by the equation y = -1/2x + 1/4
Answer:
Hey there! The answer to your question will be below
Step-by-step explanation:
The answer to your question is -1/2
-1/2x + 1/4
= -1/2
Hope that helps
By:xBrainly
help with this I don't know how to solve plz greatly appreciate
Answer:
cos∅ = 16√481/481
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
cos∅ = adjacent/hypotenuse
tan∅ = opposite/adjacent
Step 1: Find hypotenuse
15² + 16² = c²
c = √481
Step 2: Find cos∅
cos∅ = 16/√481
cos∅ = 16√481/481
An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used.
A. Find the value of the test statistic.
B. State the null and alternative hypotheses.
Answer:
A
The test statistics is [tex]t = -1.7[/tex]
B
The Null and Alternative hypothesis are
[tex]H_o : \mu = 47.2[/tex] and [tex]H_a : \mu \ne 47.2[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47.2 miles/gallon(MPG)[/tex]
The sample size is [tex]n = 250 \ van[/tex]
The sample mean is [tex]\= x = 47.0[/tex]
The sample standard deviation is [tex]\sigma = 1.9[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then
The Null Hypothesis is
[tex]H_o : \mu = 47.2[/tex]
The alternative Hypothesis is
[tex]H_a : \mu \ne 47.2[/tex]
The test statistics can be mathematically evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]
[tex]t = -1.7[/tex]
In Triangle ABC, AB = 10. AC = 14, and angle A = 51°. Find the length of BC to the nearest hundredth
Answer:
BC ≈ 10.94
Step-by-step explanation:
Base on the triangle we were given 2 sides and an angle. We were also asked to find the last length BC.
we can use cosine rule to find the side BC.
Base on cosine rule
a² = b² + c² - 2bc cos A
a = BC
b = AC = 14
c = AB = 10
a² = 14² + 10² - 2 × 14 × 10 cos 51°
a² = 196 + 100 - 280 cos 51°
a² = 296 - 280 × 0.62932039105
a² = 296 - 176.209709494
a² = 119.790290506
square root both sides
a = √119.790290506
a = 10.9448750795
BC ≈ 10.94
Answer:
BC = 10.94
Step-by-step explanation:
its a las of cosines
a² = b² + c² - 2bc cos A
AB = 10
AC = 14
angle A = 51°
BC² = 10² + 14² - (2 * 10 * 14 cos 51°)
BC = sqrt 119.8
BC = 10.94
In the xy-plane, what is the y-intercept of the graph of the equation y=V4-?
O a. 2
O b.4
O c. 16
O d. There is no y-intercept.
Answer:
D
Step-by-step explanation:
There isn't enough information to find a y-intercept.
A simple random sample of size nequals17 is drawn from a population that is normally distributed. The sample mean is found to be x overbar equals 56 and the sample standard deviation is found to be sequals10. Construct a 95% confidence interval about the population mean. The lower bound is nothing. The upper bound is nothing. (Round to two decimal places as needed.)
Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
Step(i):-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
Step(ii):-
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]
( 56 - 4.2344 , 56 + 4.2344)
(51.7656 , 60.2344)
Conclusion:-
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
The scores on an exam are normally distributed, with a mean of 85 and a standard deviation of 8. What percent of the scores are greater than 93?
Answer:
16%
Step-by-step explanation:
Find the z-score.
z = (x − μ) / σ
z = (93 − 85) / 8
z = 1
This means 93 is one standard deviation above the mean.
According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations. So 32% is either less than -1 or greater than +1 standard deviations. Normal curves are symmetrical, so 16% is greater than +1 standard deviations.
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6
Answer:
Graph is attached.
Step-by-step explanation:
We are to graph the following inequalities:
y > 2x + 4 ... (i)
x + y ≤ 6 ... (ii)
We can graph these inequalities on an online graphing calculator but its recommended that you graph them on your physical graph book.
Your graph is attached below. The shaded region is the required part.
The graph of a system of inequalities represents the solution of the inequalities
The solution to the system of inequalities is [tex]\mathbf{y > \frac 23}[/tex] and [tex]\mathbf{x \le \frac{16}3}[/tex]
The system of inequalities is given as:
[tex]\mathbf{y > 2x + 4}[/tex]
[tex]\mathbf{x + y \le 6 }[/tex]
See attachment for the graphs of [tex]\mathbf{y > 2x + 4}[/tex] and [tex]\mathbf{x + y \le 6 }[/tex]
From the graph, we have:
[tex]\mathbf{y > \frac 23}[/tex]
[tex]\mathbf{x \le \frac{16}3}[/tex]
Read more about system of inequalities at:
https://brainly.com/question/19526736
Estimate the indicated probability by using the normal approximation as an approximation to the binomial distribution. (PROBLEMS 4 & 5) 4. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.
5. In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.
Answer:
4
[tex]P(X \ge 219 ) = 0.093[/tex]
5
[tex]P(X \ge 219 ) = 0.1038[/tex]
Step-by-step explanation:
From the question we are told that
The percentage of hair dryers that are defective is p=2% [tex]= 0.02[/tex]
The sample size is [tex]n =10000[/tex]
The random number is x = 219
The mean of this data set is evaluated as
[tex]\mu = n* p[/tex]
substituting values
[tex]\mu = 10000 * 0.02[/tex]
[tex]\mu =200[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]
substituting values
[tex]\sigma = \sqrt{[200 (1 -0.02)]}[/tex]
[tex]\sigma = 14[/tex]
Since it is a one tail test the degree of freedom is
df = 0.5
So
[tex]x_l = x- 0.5[/tex]
[tex]x = 219 - 0.5[/tex]
[tex]x = 218.05[/tex]
Now applying normal approximation
[tex]P(X \ge 219 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]
substituting values
[tex]P(X \ge 219 ) = P(z > \frac{218.5 - 200}{14} )[/tex]
[tex]P(X \ge 219 ) = P(z > 1.32} )[/tex]
From the z-table
[tex]P(X \ge 219 ) = 0.093[/tex]
Considering Question 5
The random number is x = 90
The mean is [tex]\mu = n * p[/tex]
Where n = 100
and p = 0.85
So
[tex]\mu = 0.85 *100[/tex]
[tex]\mu = 85[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]
substituting values
[tex]\sigma = \sqrt{[85 (1 -0.85)]}[/tex]
[tex]\sigma = 3.5707[/tex]
Since it is a one tail test the degree of freedom is
df = 0.5
Now applying normal approximation
[tex]P(X \ge 90 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]
substituting values
[tex]P(X \ge 219 ) = P(z > \frac{89.5 - 85}{3.5707} )[/tex]
[tex]P(X \ge 219 ) = P(z > 1.2603} )[/tex]
From the z-table
[tex]P(X \ge 219 ) = 0.1038[/tex]
what is the answer to this ??
Answer:
[tex] A.\angle 1\: \\\\D. \angle 3[/tex]
Step-by-step explanation:
[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]
please help! the number of candies consumed varies inversely with the number of children present
Answer:
The answer is
210 candiesStep-by-step explanation:
Let n represent the number of children
Let c represent the number of candies
The above variation is written as
[tex]c = \frac{k}{n} [/tex]
when n = 12 c = 140
So we have
[tex]140 = \frac{k}{12} [/tex]
Cross multiply
That's
k = 1680
So the formula for the variation is
[tex]c = \frac{1680}{n} [/tex]
when n = 8
[tex]c = \frac{1680}{8} [/tex]
c = 210
Therefore there are 210 candies consumed when there are 8 children
Hope this helps you
please answer this question
Answer:
c
Step-by-step explanation:
next
In a survery of 154 households, a Food Marketing Institute found that 106 households spend more than $125 a week on groceries. Please find the 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries.
Answer:
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
PLEASE HELP ME!! A hexagon has vertices (3,1) and (4,1). The hexagon is dilated. The new hexagon has vertices (6,1) and (10,1). {In the same spots as the old hexagon}. What is the center of dilation? What is the dilation factor? I can try to add information.
Answer:
( 2,1) is the center of dilation and 4 is the scale factor
Step-by-step explanation:
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
3,1 becomes 6,1
6,1 = k( 3-a) +a, k( 1-b)+b
6 = 3k -ka+a
1 = k -kb +b
4,1 becomes 10,1
10,1 = k( 4-a) +a, k( 1-b)+b
10 = 4k -ka+a
1 = k -kb +b
Using these two equations
6 = 3k -ka+a
10 = 4k -ka+a
Subtracting the top from the bottom
10 = 4k -ka+a
-6 = -3k +ka-a
------------------------
4 = k
Now solving for a
6 = 3k -ka+a
6 = 3(4) -4a+a
6 =12 -3a
Subtract 12
6-12 = -3a
-6 = -3a
Divide by -3
-6/-3 = -3a/-3
2 =a
Now finding b
1 = k -kb +b
1 = 4 - 4b+b
1 =4 -3b
Subtract 4
-3 = -3b
Divide by -3
1 = b
Answer:
Dilation factor: 4.
Center of dilation: (2, 1).
Step-by-step explanation:
The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.
Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.
In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.
10 = 4(4 – a) + a
10 = 16 – 4a + a
10 = 16 – 3a
-3a + 16 = 10
-3a = -6
a = 2
1 = 4(1 – b) + b
1 = 4 – 4b + b
1 = 4 – 3b
-3b + 4 = 1
-3b = -3
b = 1
And so, your center of dilation will be (2, 1).
Hope this helps!
Find the length of side BC.
Give your answer to 1 decimal place.
C
14 cm
58°
Α'
B
Answer:
length of side BC = 11.9cm
The complete question found on brainly (ID: 14303570 ) is stated below:
Find the length of side BC.
Give your answer to 1 decimal place.
∠A = 58°
AC = 14cm
Find attached the diagram of the triangle.
Step-by-step explanation:
From the diagram
∠A = 58°
∠B = 90°
AC = 14cm
The triangle is a right angled triangle
To get the length side of BC, we would
apply trigonometry SOHCAHTOA.
In this question the sine ratio would be appropriate since we know the hypotenuse but we are looking for the opposite side (BC).
Sine ratio: Sin58° = opposite/hypotenuse
Sin58° = BC/AC
Sin58° = BC/14
BC = 14sin58°
BC = 14 × 0.8480
BC = 11.9cm
length of side BC = 11.9cm (1 decimal place)
8. What should be subtracted from 360 to make
it a perfect cube?
Answer:
17
Step-by-step explanation:
The closest perfect cube (to 360) is 343 (7^3) .
360-343 = 17
Subtract 17.
Answer:
You should subtract 17 from 360 to make a perfect cube
Step-by-step explanation:
What is the next item in the sequence −10,−3,4,11
Answer:
18
Step-by-step explanation:
The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!
The next item in the sequence is 18.
What is sequence and series ? A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.A number sequence is a collection of numbers that move from term to term according to a specific pattern or rule.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.
The sequence is -10 ,-3, 4, 11,........
this sequence is following pattern ,you add 7 from the previous number to get the next number
First term = -10 + 7 = -3,
Second term =-3 + 7 = 4, .
The next item will be 11 + 7 = 18.
Therefore, The next item in the sequence is 18.
Learn more about sequence brainly.com/question/12474324 here
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Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 300. (b) The weight of a Upper T dash bone steak.
Answer:
a) Discrete random variable
b) Continous random variable.
Step-by-step explanation:
a) As the number of people can take only integer values, from 0 to n (0, 1, 15, 256, for example, but not 5.6) and not decimals values, we can say that it is a discrete variable.
b) In this case, the weight of a Upper T dash bone steak is a physical variable and can take decimals positive values (0.645 lbs for example).
Then, this variable is a continous variable.
What is 1(y), when y=-7/12?
Answer: -7/12
Step-by-step explanation: an number multiplied by 1 is itself
Find the exact value
sin 79° cos 19° - cos 79° sin 19°
Step-by-step explanation:
Using the trigonometric identity
sin(a - b) = sin a cos b - cos a sin b
So sin 79° cos 19° - cos 79° sin 19° can be written as
sin ( 79 - 19) = sin 60
And
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
Hope this helps you
Find the volume of this Composite solid
Answer:
D. 569.39 m^3
Step-by-step explanation:
First, we can split up the solid into two shapes: a cone and a cylinder.
Then we can find the volume of the cone
The formula is v= pi r^2 h/3
We know the radius is four and so is the height.
Plug it in and we get 67.02 m^3
Next is the cylinder
Formula is pi r^2 h
We know that the radius is 4 and the height is 10
Plus it in and we get 502.65 m^3
We add 67.02 and 502.65 together to get the total volume.
Answer is D. 569.39 m^3
Mine is a bit higher than D since I used a pi button instead of 3.14
Using Volume Formulas: Tutorial
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Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
identical volumes? There is more than one correct answer.
B
TUX
X
Font Sizes
A. A
E JE
Square Pyramids
Rectangular Pyramid
Volume
Base Length Height
Volume
Volume x4 Base Length Base Width Height
(2x)
3
(lxwh
3
I
Characters used: 110 / 15000
Submit
Answer:
For the Square
Base length is 6 units
Height is 4 units
Volume is 48 cubic units
Volume of 4 square pyramids is 192 cubic units
(Rectangular)
Base length is 12 units
Base width is 8 units
Height is 6 units
Volume is 192 cubic units
Step-by-step explanation:
Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.
Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.
Can somebody help me with this question?
Answer:
86 yd
Step-by-step explanation:
the area of the shaded region is 2924 yd²
let b the doted side next y :
the area of the total triangle is :
A = (y+b)*68/2 = 2924+ b*68/2
[tex]\frac{(y+b)*68}{2}[/tex] = [tex]\frac{b*68}{2}[/tex] + 2924 [tex]\frac{68*(y+b-b)}{2}[/tex] = 2924 68*y/2 = 2924 68y = 2*2924 y= (2*2924)/68 y= 86 ydIn the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 120 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population?
Required:
a. State the random variable, population parameter, and hypotheses.
b. State the Type I and Type II errors in the context of this problem.
Answer:
(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
Step-by-step explanation:
A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.
From past data, it is believed that 11% of all Americans are left-handed.
The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.
(a)
The hypothesis can be defined as follows:
H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.
Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.
And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.
Which inequality is represented by the graph?
Answer:
y <= (2/5)x - 3/2
Step-by-step explanation:
y-intercept is -3/2
slope = 2/5
shading is below the line
Answer: y <= (2/5)x - 3/2
The second statement is the ___ of the first. a⇒b b⇒a A) converse B) contrapostive C) contradition D) inverse
Answer:
A. converse
Step-by-step explanation:
Let's first define some concepts:
Statement If p , then q
Converse If q , then p
Inverse If not p , then not q
Contrapositive If not q , then not p
From the statement we have:
a ⇒b
b ⇒a
if you look at the definitions then:
The second statement is the converse of the first
Answer:
Converse
Step-by-step explanation:
Got Correct On ASSIST.
Not sure how to solve
Answer:
B. zero
Step-by-step explanation:
The slope of a line can be computed as ...
slope = rise/run
When the line is horizontal, the "rise" is zero over any "run", so the slope is zero.
the commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. if a random sample of 37 workers is taken and results in a sample mean of 31 minutes and sample standard deviation of 5 minutes, find a 95% confidence interval estimate for the population mean using the student's t-distribution.
Answer:
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 37 - 1 = 36
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0262
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0262\frac{5}{\sqrt{37}} = 1.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 31 - 1.67 = 29.33 minutes
The upper end of the interval is the sample mean added to M. So it is 31 + 1.67 = 32.67 minutes.
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.