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
Lorico [155]
3 years ago
12

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard dev

iation of 0.2 inches. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long
Mathematics
1 answer:
Vladimir [108]3 years ago
7 0

Answer:

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

                Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean = 30.05 inches

           \sigma   = standard deviation = 0.2 inches

             n = sample of sheets = 4

So, Probability that average length of a sheet is between 30.25 and 30.35 inches long is given by = P(30.25 inches < X bar < 30.35 inches)

P(30.25 inches < X bar < 30.35 inches)  = P(X bar < 30.35) - P(X bar <= 30.25)

P(X bar < 30.35) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{30.35-30.05}{\frac{0.2}{\sqrt{4} } } ) = P(Z < 3) = 0.99865

 P(X bar <= 30.25) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } <= \frac{30.25-30.05}{\frac{0.2}{\sqrt{4} } } ) = P(Z <= 2) = 0.97725

Therefore, P(30.25 inches < X bar < 30.35 inches)  = 0.99865 - 0.97725

                                                                                       = 0.0214

                                       

You might be interested in
What is the mathematical name for the object that is defined by the Crocodile River?
kipiarov [429]
The correct answer is : line y=4
6 0
3 years ago
Read 2 more answers
DUE TOMORROW GIVING BRAINLIEST!
Stells [14]

Answer:

I gotcha.

Step-by-step explanation:

Condensation - water which collects as droplets on a cold surface when humid air is in contact with it.

Pressure - continuous physical force exerted on or against an object by something in contact with it.

Temperature - the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

Thermal energy - (also called heat energy) is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other. The energy that comes from the temperature of the heated substance is called thermal energy.

<h2>there</h2>
6 0
3 years ago
Read 2 more answers
Here is a system of equations:
laila [671]

Answer:

y = -10

Step-by-step explanation:

(-7x+3y) - (-7x +10y) =-65 -(-135)

-7x + 3y + 7x -10y = 70

-7y = 70

y = -10

7 0
3 years ago
Read 2 more answers
Need help???! Explanation too please
Natalija [7]

Answer:

When X=Y every number on either side is the same, for example 1(X)=1(Y)

Step-by-step explanation:

This is because when X=Y the X value isn't altered in any way to equal Y, so they are the same number, hope this helped!

4 0
3 years ago
i need help with number 7. its solving systems of equations by substitution. please show work!!! i need help
SIZIF [17.4K]
#7:
<span>Subtract </span>y<span> from both sides:
</span>-4x=6-y

Divide both sides by -4:

Answer:
x= -6-y/4


#7 part 2:

Add <span>y</span><span> to both sides:
</span>-5x=21+y

Divide both sides by -5:

Answer: x=-21+y/5

hope i helped!



7 0
3 years ago
Other questions:
  • Which of the following triangle lengths form right triangles? Select all that apply.
    10·2 answers
  • Using your knowledge of circles, label the following on the given diagram: chord, tangent, radius, secant, point of tangency and
    5·1 answer
  • Caleb purchases 5 beach towels for d dollars each. Each towel is charged an additional 6% sales tax.
    7·1 answer
  • Q # 28 please help.Use a calculator to find the value
    9·2 answers
  • Find the volume and surface area of a cube with sides 6 inches long?
    11·1 answer
  • How do you find the width of a number when you have the feet and total area
    15·2 answers
  • Expand the expression.<br> -7(k - 3)<br> -7k + 21<br> -k – 21<br> k+ 21<br> -7k - 21
    6·1 answer
  • MATH............................................................
    9·2 answers
  • Raffia went shopping for new furniture he bought a couch for $750 and a mattress for 950 dollars. When he came home he had $350
    5·2 answers
  • Work is due in 2 hours​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!