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
iren2701 [21]
2 years ago
13

Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm an

d a standard deviation of 0.002 mm. A new book will be printed on 500 sheets of this paper. Approximate the probability that the
Mathematics
1 answer:
marusya05 [52]2 years ago
6 0

Answer:

The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

Step-by-step explanation:

The complete question is:

Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.

Solution:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{S}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

\sigma_{S}=\sqrt{n}\sigma

The information provided is:

n=500\\\mu=0.1\\\sigma=0.002

As <em>n</em> = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.

So, the total thickness of the book (S) will follow N (50, 0.045²).

Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:

P(49.9

                               =P(-2.22

Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

You might be interested in
How many 5/8 -foot pieces of wood can you cut from a board that is 4/5/8 ft long?
Vadim26 [7]

Answer:

7

Step-by-step explanation:

4 5/8 divided by 5/8 = 7 2/5

3 0
2 years ago
What decimal is represented by this expanded form?
Mnenie [13.5K]

Answer:

53028.064 I think

Step-by-step explanation:


6 0
3 years ago
Which number goes in the blank?
uranmaximum [27]

Answer:

A

Step-by-step explanation:

842,109 is bigger then 842,019

8 0
2 years ago
The mpg (miles per gallon for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8. w
lesantik [10]
For this Q:

mean=31
st.dev.=0.8
x=32

Calculate z-score:
z=(x-m)/s = (32-31)/0.8=1.25

This z-score value corresponding to the probability of 0.8944

<span />
6 0
3 years ago
A percentage is a fractional value expressed as the number of
enyata [817]
In mathematics, a percentage (from Latin per centum "by a hundred") is a number or ratio expressed as a fraction of 100.
3 0
3 years ago
Other questions:
  • The submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise 63 feet and then
    13·1 answer
  • You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
    8·1 answer
  • Norris threw a plastic toy in the tub for her dog. But there is a problem; the puppy does not like putting his face in water.
    13·1 answer
  • An architect has a scale drawing of a back porch that has a length and a width of 36 x 75 feet. If the Architect’s drawing is 4
    11·1 answer
  • Ms. Anderson deposits $700 into a savings account that pays a simple interest of 2% per year. Which of the following would be th
    6·2 answers
  • Paula drew this plan for a new backyard shed. each unit is 1 foot. what is the perimeter of the shed?
    15·1 answer
  • You can get these points for free but I hope you would help at least 1 person on here and answer their problem.
    8·2 answers
  • Find the measure of each acute angle.<br> 3xº<br> 2x<br> 19<br> 3.2<br> and 20
    11·2 answers
  • Imagine you are an architect hired by a newly elected mayor to design a city. What questions might you have for the mayor before
    9·1 answer
  • 2.5 x 10⁻⁴<br> Give an explanation on how to do the answer and subject please for brainliest
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!