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Sergio [31]
3 years ago
5

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 stand

ard deviation 0.01 mm. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)
Mathematics
1 answer:
LenaWriter [7]3 years ago
7 0

Answer:

10.20% probability that a randomly chosen book is more than 20.2 mm thick

Step-by-step explanation:

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.

In this problem, we have that:

250 sheets, each sheet has mean 0.08 mm and standard deviation 0.01 mm.

So for the book.

\mu = 250*0.08 = 20, \sigma = \sqrt{250}*0.01 = 0.158

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}

Z = \frac{20.2 - 20}{0.158}

Z = 1.27

Z = 1.27 has a pvalue of 0.8980

1 - 0.8980 = 0.1020

10.20% probability that a randomly chosen book is more than 20.2 mm thick

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The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

<h3>Determining the perimeter and area of the triangle giving line equation</h3>

In order to determine the area and perimeter of the lines, we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

The points of intersection of the line are;

(x₁, y₁) = (- 0.4, 5.2),

(x₂, y₂) = (-0.8, 4.4),

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Determine the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

Determine the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

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Perimeter = (2√10 + 4√5) / 5 units

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A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/12010318

#SPJ1

3 0
1 year ago
Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent​ switc
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Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent​ switches, each one set on or off. The receiver​ (wired to the​ door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches​ independently.<u>The probability of at least one pair of neighbors using the same​ settings is 0.65633</u>

Step-by-step explanation:

<u>Step 1</u>

In the question it is given that

Automatic garage door opener utilizes a transmitter control with four independent​ switches

<u>So .the number of Combinations possible with the Transmitters </u>=

2*2*2*2= 16

<u> Step 2</u>

Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.

= 1- 16*15*14*13*12*11/(16^6)

<u> Step 3</u>

Probability of at least one pair of neighbors using the same settings=

= 1- 0.343666

<u> Step 4</u>

<u>So the probability of at least </u>one pair of neighbors using the same settings

is  0.65633

3 0
3 years ago
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