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
Sever21 [200]
2 years ago
7

6. (4.11.2) A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08

mm and standard deviation 0.01 mm. a. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)
Mathematics
1 answer:
Maksim231197 [3]2 years ago
3 0

Answer:

10.38% probability that a randomly chosen book is more than 20.2 mm thick

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 are 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 sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n elements, the mean is n\mu and the standard deviation is s = \sqrt{n}\sigma

In this problem, we have that:

\mu = 250*0.08 = 20, \sigma = \sqrt{250}*0.01 = 0.1581

What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)

This is 1 subtracted by the pvalue of Z when X = 20.2. So

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

By the Central Limit Theorem

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

Z = \frac{20.2 - 20}{0.1581}

Z = 1.26

Z = 1.26 has a pvalue of 0.8962

1 - 0.8962 = 0.1038

10.38% probability that a randomly chosen book is more than 20.2 mm thick

You might be interested in
If two sides of a triangle are 6 and 8 the third side could be
-Dominant- [34]
3,4,5 are Pythagorean triplets. then 6,8,10 are, so the answer is 10
<span />
6 0
3 years ago
Find value of the variable
just olya [345]

Answer:

x=10

Step-by-step explanation:

16/24=(x-2)/12

or, 16/2=x-2

or, 8=x-2

or, x-2=8

or, x=10

Answered by GAUTHMATH

7 0
3 years ago
students need to paint 500 pumpkins for the fair. They already painted 193. How many pumpkins are left to paint?
lys-0071 [83]
You would subtract the the amount painted from 500.
500-193=307
They have to paint 307 more.
3 0
3 years ago
Read 2 more answers
7. The probability that a randomly chosen student will be left-handed is .09: a) In a class of 108, find the probability that th
vampirchik [111]

Solution :

Let x be student will be left handed

P = 0.09

Using the normal approximation to binomial distribution,

a). n = 108,

    μ = np = 9.72

    $\sigma = \sqrt{np(1-p)}$

       $=\sqrt{8.8452}$

       = 2.9741

Required probability,

P(x=8) = P(7.5 < x < 8.5)

$=P\left(\frac{7.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{8.5-9.72}{2.9741}\right)$

$=P(-0.75 < z < -0.41)$

Using z table,

= P(z<-0.41)-P(z<-0.75)

= 0.3409-0.2266

= 0.1143

b). P(x=12) = P(11.5 < x < 12.5)

$=P\left(\frac{11.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{12.5-9.72}{2.9741}\right)$

$=P(0.60 < z < 0.94)$

Using z table,

= P(z< 0.94)-P(z< 0.60)

= 0.8294 - 0.7257

= 0.1006

7 0
3 years ago
Suppose that the function f(x) = 2x + 15 represents the cost to rent x movies a month from an internet movie club.
kolbaska11 [484]
She needs 19 more dollars because the amount that the entire thing costs is 29
7 0
3 years ago
Other questions:
  • Solve for y, y-8= -( y-2) / 2
    12·2 answers
  • When I ask my calculator for a decimal value of √2, it displays 1.414213562. What is the meaning of this number? To check whethe
    14·1 answer
  • The mass of a bronze statue is 15,000 g. The density of bronze is about 8 g/cm^3. What is the volume of the bronze statue?
    7·1 answer
  • A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote
    10·1 answer
  • I NEED EMERGENCY SOS
    11·1 answer
  • Solve:<br> X + y = 4<br> -5x - 6y = -18
    10·2 answers
  • How would I solve this Rational Equation? <br><br>Solve for all values of x.
    7·1 answer
  • Find the area of the kite
    11·2 answers
  • I need help so bad please !!???
    12·1 answer
  • Solve for t.......<br><img src="https://tex.z-dn.net/?f=4%20%28t%20%2B%20%5Ccfrac%7B1%7D%7B4%7D%20%5C%3A%20%20%29%20%3D%203" id=
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!