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
BartSMP [9]
3 years ago
9

Ask Your Teacher The level of nitrogen oxides (NOX) in the exhaust after 50,000 miles or fewer of driving of cars of a particula

r model varies Normally with mean 0.08 g/mi and standard deviation 0.01 g/mi. A company has 36 cars of this model in its fleet. What is the level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01? (Hint: This requires a backward Normal calculation. Round your answer to three decimal places.)
Mathematics
1 answer:
Georgia [21]3 years ago
4 0

Answer:

The level is L = 0.084

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 0.08, \sigma = 0.01, n = 36, s = \frac{0.01}{\sqrt{36}} = 0.0017

What is the level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01?

This is X when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.325.

Z = \frac{X - \mu}{\sigma}

By the Central limit theorem

Z = \frac{X - \mu}{s}

2.325 = \frac{X - 0.08}{0.0017}

X - 0.08 = 2.325*0.0017

X = 0.084

The level is L = 0.084

You might be interested in
A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
creativ13 [48]

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

r=\frac{18}{2+\theta}

step 2

Find the value of s

s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

6 0
3 years ago
If the radius of a circle is 16 units, what is its area? (Use pie for it)
krok68 [10]

Answer:

804.25unit^2

Step-by-step explanation:

A=\pi r^2\\=\pi 16^2\\=804.25unit^2

3 0
3 years ago
Read 2 more answers
Coner earns $9 an hour for yard work.He earned $29.25.how much does he earn every minute.
makvit [3.9K]

He earns $0.15 every minute.  There are 60 minutes every hour and you are trying to found out how much money he is making in 1 minute, so you divide 9 by 60, which will give you the decimal number 0.15. The $29.25 was just a little extra information to try to brush you off.

3 0
3 years ago
Read 2 more answers
Computer geometric modeling is used regularly to help design solid figures we see and use every day. Software programs use techn
Stella [2.4K]

The geometric modeling is analyzed below.

<h3>How to illustrate the information?</h3>

Basic shapes are generally created using points, lines, circles, and triangles. Some basic shapes are rectangles, ellipses, triangles, and curves.

In geometric modeling, we make a cad model of parts for virtual analysis. By geometric modeling, one can model, and perform CAE analysis to optimize the product.

The best part is the period of doing all this is very small compared to practical manufacturing and looking at the product. In CAD one can very quickly alter the design and come up with new concepts in a very small span of time.

Here chances of error can be shorted easily and there is no wastage of material hence cost saving is there compared to practically manufacturing the part and altering it.

Learn more about modelling on:

brainly.com/question/28015639

#SPJ1

5 0
2 years ago
Find the number of real number solutions for the equation. x^2+5x+7=0
koban [17]

Given a quadratic equation ax^2+bx+c=0, we define the discriminant as

\Delta = b^2-4ac

The number of real solutions of the equation depend on the sign of \Delta:

  • If \Delta>0 the equation has two solutions
  • If \Delta=0 the equation has one double solution
  • If \Delta the equation has no real solutions

In this case, we have

\Delta = 25-28=-3

And so this equation has no real solutions.

7 0
3 years ago
Other questions:
  • Suppose that a random sample of size 36 is to be selected from a population with mean 43 and standard deviation 6. What is the a
    10·1 answer
  • Can u tell me the answers and how u got them? <br>questions 23-27<br>thx
    6·2 answers
  • A small piece of metal weighs 0.77gram.What is the value of the digit in the tenths place
    10·2 answers
  • Which expression is a trinomial?<br> 2x² + 2x - 4<br><br> 7x^3 - 2X<br><br> 50x<br><br> 2x²
    11·2 answers
  • Which factors is multiplied and give you 24 and when added gives you -4
    5·1 answer
  • I need help on this. Thanks,<br><br> (picture attached)
    10·1 answer
  • Plzzz help<br> thank u for those who help
    5·1 answer
  • Determine the type of solution you will have if you get -6=6
    14·1 answer
  • Stop &amp; Shop has a sale on pasta. Casa Pasta was on sale for 8 boxes for $10.99. The store brand Stop &amp; Shop Pasta was al
    9·1 answer
  • The table below shows a record of three Baloon Pop games.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!