1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Black_prince [1.1K]
3 years ago
6

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and test

ed them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers.
Find a 95% confidence interval on mean tire life.
Mathematics
2 answers:
lesya692 [45]3 years ago
7 0

Answer:

60139.7-2.131\frac{3645.94}{\sqrt{16}}=58197.33    

60139.7+2.131\frac{3645.94}{\sqrt{16}}=62082.07    

So on this case the 95% confidence interval would be given by (58197.33;62082.07)    

Step-by-step explanation:

Previous notation

\bar X= 60139.7 represent the sample mean

\mu population mean (variable of interest)

s=3645.94 represent the sample standard deviation

n=16 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=16-1=15

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,15)".And we see that t_{\alpha/2}=2.131

Now we have everything in order to replace into formula (1):

60139.7-2.131\frac{3645.94}{\sqrt{16}}=58197.33    

60139.7+2.131\frac{3645.94}{\sqrt{16}}=62082.07    

So on this case the 95% confidence interval would be given by (58197.33;62082.07)    

frutty [35]3 years ago
3 0

Answer:

The 95% confidence interval for mean tire life is between 52,368.4 kilometers and 67,911 kilometers.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the students t-distribution to solve this question.

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 = 16 - 1 = 15

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.68

The margin of error is:

M = T*s = 2.1315*3645.94 = 7771.3

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 60139.7 - 7771.3 = 52,368.4.

The upper end of the interval is the sample mean added to M. So it is 60139.7 + 7771.3 = 67,911.

The 95% confidence interval for mean tire life is between 52,368.4 kilometers and 67,911 kilometers.

You might be interested in
Explain how you can finding 4 384
kkurt [141]
There are a lot of ways you can do this, depending on what numbers you use, you can divide, multiply, add, or subtract to get 4,384, did you mean a specific term of math?<span />
8 0
3 years ago
Read 2 more answers
PLEASE ANSWER ASAP!!!! MUST BE CORRECT FOR POINTS GIVEN!!!!! THE QUESTION IS BELOW IN THE SCREENSHOT!!!!! VERY IMPORTANT!!!!!
AfilCa [17]
The answer is D:6 because you divide by 3
3 0
3 years ago
Read 2 more answers
Given functions f(x)=3x^2, g(x)= x^2-4x+5, and h(x)=-2x^2+4x+1<br> Rank them from least to greatest
Sindrei [870]
Ok, ranked by axis of symmetry

basically x=something is the axis of symmetry
the way to find the axis of symmetry is to convert to vertex form and find h and that's the axis of symmetry

but there's an easier way

for f(x)=ax^2+bx+c
the axis of symmetry is x=-b/2a
nice hack my teacher taught me


so

f(x)=3x^2+0x+0
axis of symmetry is -0/(3*2), so x=0 is the axis of symmetry for f(x)

g(x)=1x^2-4x+5,
axis of symmetry is -(-4)/(2*1)=4/2=2, x=2 is axis of symmetry for g(x)


h(x)=-2x^2+4x+1
axis of symmetry is -4/(2*-2)=-4/-4=1, x=1 is the axis of symmetry for h(x)


0<1<2
axisies
f(x)<h(x)<g(x)

order based on their axises of symmetry is f(x), h(x), g(x)
8 0
3 years ago
Can someone check these answers for me
Salsk061 [2.6K]
Hun, these questions look opinionated. They are asking what all you can do and what you need help with.
5 0
3 years ago
I don't know how to do this please help explain how to do it aswell as give the answer so i understand
Zinaida [17]

<u>We are given:</u>

The function: y = -16t² + 64

where y is the height from ground, t seconds after falling

<u>Part A:</u>

when the droplet would hit the ground, it's height from the ground will be 0

replacing that in the given function:

0 = -16t² + 64

16t² = 64                          [adding 16t² on both sides]

t² = 4                                [dividing both sides by 16]

t = 2 seconds                  [taking square root of both sides]

<u>Part B:</u>

for second droplet,

height from ground = 16 feet

time taken = t seconds

acceleration due to gravity = 10 m/s²

initial velocity = 0 m/s

h = ut + (1/2)at²                 [second equation of motion]

16 = (0)(t) + (1/2)(10)(t²)

16 = 5t²

t² = 16/5

t = 1.8 seconds (approx)

Therefore, the second droplet takes the least amount time to hit the ground

4 0
3 years ago
Other questions:
  • Do you guys know how to remember certain measurements?
    14·1 answer
  • A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many triangles can be drawn that fit this description?
    10·2 answers
  • The sum of two numbers is 42, and one number is twice the other. Find the two numbers​
    11·2 answers
  • Which of the following equals 0.000001? <br> 1 x 10-5 <br> 1 x 10-6 <br> 1 x 10-7 <br> 1 x 10-8
    12·2 answers
  • The point (5, -1) is a solution of the equation: y = 2x − 11 question 28 options: true false
    7·1 answer
  • 30 points Please help will mark brainliest.
    6·1 answer
  • What is ((-1²-3)²+2•8​
    14·1 answer
  • Caroline bought movie tickets for three Children and a bucket of popcorn for $9.50. If she spent a total of $35.75, how much was
    10·1 answer
  • What equation best represents the following sentence?
    6·1 answer
  • Hallar la altura(h) de un triángulo que tiene una base 12 metros y un área de 96
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!