Mathematics, 14.04.2020 18:27 katiepotter

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)

Answers: 1

Show answers

Answers

Answer from: lexhorton2002

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

Answer from: Quest

Heidi’s has to come to a party tomorrow night at the navy house i was like going home i have ig

Answer from: Quest

let x and 400 - x be the two numbers.

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.

< ==> 0.80x + 0.85(400 - x) = 400 - 68

==> 340 - 0.05x = 332

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 20:00, ladybugys

Use circumcenter theorem to solve for the given values

Answers: 3

continue

Mathematics, 21.06.2019 20:00, faithyholcomb

Someone answer asap for ! max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a. the median of max’s data is 250 b. more than half of the data points max recorded were 177 centimeters. c. a data point chosen at random is as likely to be above the mean as it is to be below the mean. d. every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 1

continue

Mathematics, 21.06.2019 20:30, cheating53

Kayaks rent for $35 per day. which expression can you use to find the cost in dollars of renting 3 kayaks for a day?

Answers: 1

continue

Mathematics, 21.06.2019 21:50, roxanneee2145

5. which description does not guarantee that a quadrilateral is a squar ajo is a parallelogram with perpendicular diagonals 0% has all sides congruent and all angles congruent o has all right angles and has all sides congruent 10% is both a rectangle and a rhombus 30%

Answers: 2

continue

You know the right answer?

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