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
dangina [55]
3 years ago
9

The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A

random sample of 11 vehicles is taken and results in a sample mean of 65 miles per hour and sample standard deviation of 9 miles per hour. Determine and interpret the 90% confidence interval for the mean speeds of vehicles traveling on the highway.
Mathematics
1 answer:
Maksim231197 [3]3 years ago
3 0

Answer:

The 90% confidence interval would be given by (60.09;69.91)    

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X =65 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size  

2) Confidence interval

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=11-1=10

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that t_{\alpha/2}=1.81

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

65-1.81\frac{9}{\sqrt{11}}=60.09    

65+1.81\frac{9}{\sqrt{11}}=69.91

So on this case the 90% confidence interval would be given by (60.09;69.91)    

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

You might be interested in
A 10 ft vertical post casts a 16 in shadow At the same time a nearby cell phone tower cast a 124 ft shadow
chubhunter [2.5K]
10/16=x/124
X=(124)(10)/(16)=1240/16=80
5 0
3 years ago
Help with trigonometry​
diamong [38]

Answer:

cos ∠CBD = - 4√41 / 41

Step-by-step explanation:

AB = 4      ΔABC = (4 x AC) / 2 = 10

AC = 5

BC = √5² + 4² = √41

cos ∠CBD = cos (180° - ∠CBA) = cos 180° cos ∠CBA + sin 180° sin ∠CBA

(cos 180° = - 1          sin 180° = 0       cos ∠CBA = 4 / √41 )

cos ∠CBD = (-1) x cos  ∠CBA = - 4 / √41 = - 4√41 / 41

4 0
3 years ago
Look I have like barely any points can someone help answer this tho
MariettaO [177]

Answer:

3.5

Step-by-step explanation:

These are similar triangles.

BC:AC = BD:AD

6:5  is the ratio.

Then, simply multiply:

4.2 x 5/6 = 3.5

So, x = 3.5!

5 0
3 years ago
SOMEONE PLZZZ HELP ME PLZZZZZZ
qaws [65]

Answer:

hiii

Step-by-step explanation:

=-8

7 0
3 years ago
Read 2 more answers
How much principal must be deposited to earn $1000 simple interest in 2 years at a rate of 5%
Murrr4er [49]

Answer:

1100                                                                 brainliest please

Step-by-step explanation:

1000×2×0.05=100

1000+100=110

4 0
3 years ago
Other questions:
  • A European automobile has a gas mileage of 16km/L .. What is the gas mileage in miles per gallon?. Express your answer using two
    5·1 answer
  • -12 = 3x + 3 here it is just for you
    13·2 answers
  • Convert 147% to a fraction in simplest form​
    12·1 answer
  • Billie and toni are driving from chicago to phoenix. the first day they drove 420 miles. they want to drive at 65 miles per hour
    5·1 answer
  • A rectangular sandbox has an area of 3x square inches. If the width of the sandbox is x inches, what is the length of the sandbo
    11·1 answer
  • You roll two number cubes.
    7·2 answers
  • EASY TRUE OR FALSE QUESTION
    10·2 answers
  • #1 need help asap plzzzzzzzzzzzz
    15·1 answer
  • How many sides does a polygon have if the measure of each exterior angle is 9? What is the sum of the measure of each of the int
    7·1 answer
  • Brainliest to first person WHO GETS IT RIGHT.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!