A certain type of aluminum screen has, an average, one flaw in a 100-foot roll. Assume the flaw distribution approximately follows the Poisson distribution. (a) Find the probability that a 100-foor roll has at most 2 flaws. (b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them. (c) Suppose that a store had many 200-foot rolls in storage, a clerk is doing inspections. What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it
Answer:
a) 0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.
b) 0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.
c) 0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it.
Step-by-step explanation:
To solve this question, we need to understand the Poisson and the Binomial distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
(a) Find the probability that a 100-foor roll has at most 2 flaws.
A certain type of aluminum screen has, an average, one flaw in a 100-foot roll, which means that [tex]\mu = 1[/tex]. Only one roll means that the Poisson distribution is used.
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1}*1^{0}}{(0)!} = 0.3679[/tex]
[tex]P(X = 1) = \frac{e^{-1}*1^{1}}{(1)!} = 0.3679[/tex]
[tex]P(X = 2) = \frac{e^{-1}*1^{2}}{(2)!} = 0.1839[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3679 + 0.3679 + 0.1839 = 0.9197[/tex]
0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.
(b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them.
Two parts.
Probability that a single 200-foot roll has no flaw.
This is [tex]P(X = 0)[/tex], Poisson(single 200-foot roll) when [tex]\mu = \frac{200*1}{100} = 2[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
0.1353 probability that a single 200-foot roll has no flaw.
Probability that on 10 200-foot rolls, 3 have no flaws.
Multiple 200-foot rolls means that we use the binomial distribution.
0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]
10 200-foot rolls means that [tex]n = 10[/tex]
We want [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.1353)^{3}.(0.8647)^{7} = 0.1074[/tex]
0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.
(c) What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it.
0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]
2 with flaws in the first 14, which is [tex]P(X = 2)[/tex] when [tex]n = 14[/tex]
The 15th has no flaw, with probability of 0.1353. So
[tex]P = 0.1353*P(X = 2) = 0.1353*(C_{14,2}.(0.1353)^{2}.(0.8647)^{12}) = 0.1353*0.2911 = 0.0394[/tex]
0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it
The area of a rectangular field of length 12 m is 108 sq.m
Find the width of the field.
Answer:
width of rectangle is 9m
For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item
Answer:
a) According to probability theory, the following are possible:
(1) The probability that a customer will buy 5 items in a single purchase is 30%. This represents a 0.30 chance of the customer buying 5 items.
(3) The probability that a customer will buy 3 items in a single purchase is 99% This means that there a 0.99 chance that the customer will buy 3 items.
b) According to probability theory, the following are not possible:
2) The probability that a customer will buy 3 items in a single purchase is 101%. Probability is always equal to 1 or 100%. It cannot exceed 100%.
(4) The probability that a customer will buy 8 item. This part lacks the necessary information to solve the problem.
Step-by-step explanation:
Probability describes the likelihood or chance of an event happening out of the many possible events that can take place. The sum of all probabilities for a particular event is always equal to 1. This shows that probability does not exceed 100%.
f(x) = 4x - 12
F1(x)=
Work out the surface area of this cylinder.
12 cm
35 cm
Answer:
The surface area of this cylinder is 3545 cm²
∵ π =
∴ The lateral area = 24 × × 35.
∴ The area of the base = × (12)² = (144) = 452 cm²
∴ The surface area = 2640 + 2(452 ) = 3545 cm²
∴ The surface area of this cylinder is 3545 cm²
Step-by-step explanation:
Hope it is helpful.....
If f ( x ) = 1 3 x − 5 , what is f ( − 6 ) ?
Answer:
-4
Step-by-step explanation:
by finding the exact value.
PLEASE HELP MEE ITS URGENT
Read the sentences below. They are the first part of a summary of the article. Atoms are the building blocks of everything. They are too tiny to be seen. Atoms are made up of electrons, protons and neutrons. Which answer BEST completes the summary? A Each atom has a special number and element B Each atom has some oxygen and hydrogen. с Each atom has an atomic number of 1. D Each atom is made up of 100 elements.
Answer:
A (i think)
Step-by-step explanation:
If i'm right please mark me branliest
Craft project
Mariah has the pool of ribbon shown at the right and 1/2 yard of fabric for a craft project. She wants to cut the ribbon into 6 equal pieces. How long is each piece of ribbon?
Question:
6: Find the length of each ribbon piece in inches. Show your work.
Answer:
the answer is 1 over 12
Which fraction is equivalent to a repeating decimal? A. 1/8 B. 2/8 C. 14/21 D. 3/10
Answer:
C
Step-by-step explanation:
14/21 = 2/3 = .666666666666666666666.....7
lol please help i literally cannot do math to save my life
Answer:
[tex]\displaystyle d \approx 3.6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian Plane
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point A(-2, 1)
Point B(1, -1)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(1+2)^2+(-1-1)^2}[/tex][Distance] [√Radical] (Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(3)^2+(-2)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{9+4}[/tex][Distance] [√Radical] Add: [tex]\displaystyle d = \sqrt{13}[/tex][Distance] [√Radical] Evaluate: [tex]\displaystyle d = 3.60555127546[/tex][Distance] Round: [tex]\displaystyle d \approx 3.6[/tex]Answer:
3.6 units
Step-by-step explanation:
Point A --> [tex]x_{1} \\[/tex] = -2 , [tex]y_{1}[/tex] = 1
Point B --> [tex]x_{2}[/tex] = 1 , [tex]y_{2}[/tex] = -1
AB =
[tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 } \\\sqrt{[1 - (-2)]^2 + [(-1) - 1]^2} \\\sqrt{3^2 + (-2)^2} \\\sqrt{9 + 4} \\ \sqrt{13} \\3.605[/tex]
distance between AB can be rounded to 3.6 units
Hope it helps.
Can someone please help meeeee I’m desperate
PLEASE PLEASE PLEASE HURRY!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!!!! Which TWO ARE CORRECT?
Answer: D and E I'm sure
Round 117.22666 to the nearest tenths
Answer:
117.2
Step-by-step explanation:
I hope this helps a little bit.
In a certain country, the true probability of a baby being a boy is 0.519. Among the next nine randomly selected births
in the country, what is the probability that at least one of them is a girl?
Answer:
0.9973
Step-by-step explanation:
Given :
Probability of girl, probability of success , 1 - p = 1 - 0.519 = 0.481
1 - p = 0.481
n = 9
Probability that atleast one is girl
Usingbthe binomial probability distribution :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
USing the binomial probability calculator :
p(x ≥ 1) = p(x=1) + p(x=2) + p(x=3) + p(x=4) + p(x=5) + p(x=6) + p(x=7) + p(x=8) + p(x=9)
p(x ≥ 1) = 0.9973 ( from calculator).
Please help now due in 25 minutes!!!
Answer:
y=8x+1
Step-by-step explanation:
The slope is a positive 8 because the line is going upwards. Slope equals rise over run. The rise is 8 units, and the run is 1 positive unit since it is going to the right. So 8/1 is 1. There's a +1 in the equation because the y-intercept is at positive 1. The y-intercept is where the line crosses the y-axis (vertical line). Here, the line crosses it at 1.
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Question 3 of 28
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B85B9..
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Tect
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rrect
IMG_90
The accompanying table contains the individual demand schedules of dark chocolate for Vanessa and Angela. Assuming
they are the only people in the market for dark chocolate, place each of their individual demand curves and the market
demand curve at the correct locations on the accompanying graph.
Price of dark
Pounds of dark chocolate Pounds of dark chocolate
chocolate
demanded by Vanessa
demanded by Angela
(per pound)
$8
1
3
%
IMG 90
00%
$1
3
5
orrect
0%
Market for Dark Chocolate
10
0%
Vanessa
Angela
Market
9
0%
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please help me find the missing side !
Answer:
x=14 and y=7
Step-by-step explanation:
This is a 30-60-90 triangle
So in terms of x it would be [tex]x-x\sqrt{3} -2x[/tex]
If across the 60 is [tex]7\sqrt{3}[/tex] then y would be 7 which is across the 30 degrees
And x would be 14 because 2(7)=14
What are the four
parts of axiomatic system?
An axiomatic system consists of some undefined terms (primitive terms) and a list of statements, called axioms or postulates, concerning the undefined terms. One obtains a mathematical theory by proving new statements, called theorems, using only the axioms (postulates), logic system, and previous theorems.
Hope this helps have a awesome night/day❤️✨
Step-by-step explanation:
HELP HELP 100 POINTS!! Paola was given the equation y= -x + 3. Which of following is an equivalent representation of the equation.
i also need a explanation
Answer:
no answer choices i cant help
Step-by-step explanation:
moan
A circle has a diameter of 16 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
Question 7 options:
803.84 cm2
50.24 cm2
200.96 cm2
Answer:
Step-by-step explanation:
Area of a circle=πr²
Radius = 16/2=8 Area of a circle=3.14×8×8
= 3.14×64
= 200.96cm²
= 201 cm² to the nearest unit.
A rectangular prism has a length of 14ft, a height of 8ft, and a width of 15ft. What is
its volume, in cubic ft?
Answer:
37
Step-by-step explanation:
14 + 8 + 15
Answer: 1680³
Step-by-step explanation:
length x width x height
14 x 15 x 8
A mixture of nuts contains 1 cup of walnuts for every 3 cups of peanuts write a linear equation that represents the relationships between penuts,x, and walnuts,y, Graph the line
Answer:
surfaces curving inward, so it makes parallel light rays curve outward or diverge. That's why concave lenses are sometimes called diverging lenses. ... The distance from the center of the lens to the focal point is, again, the focal length of the lens.
Step-by-step explanation:
(20 points)
What is the value of x?
☁︎
A:10
☁︎
B:20
☁︎
C:12
☁︎
D:15
Answer:
honestly I don't know 5
Step-by-step explanation:
5/8+1/4 plz help me
What is the equation of the circle with a radius of 4 and a center at (3, 2) ?
Answer:
(x - 3)^2 + (y + 2)^2 = 16
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
r = radius
(h, k ) is center of circle.
The center of the circle is (3, 2) and r is 4.
(x - 3)^2 + (y + 2)^2
16
Best of luck :3
Help me plz and thank u
Answer:
18
Step-by-step explanation:
triangle formula = b x h /2
half of 8/2= 4
9 x 4= 36
36/2= 18
Of the 800 people at a concert, 42% of them were teenagers. How many teenagers were at the concert
Answer:
336 of them were teenagers
Answer:
There are 336 teenagers at the concert.
Step-by-step explanation:
You are welcome
Let's say we have a box with 6 marbles: 3 red, 1 blue, 1 green, and 1 yellow. What is the probability of picking a yellow marble, keep it, and then
picking a blue marble?
A 1/12
B 1/30
C 1/36
D 1/11
Is 17—6x a expression or Equation
Answer:
expression because an equation has to have a plus +×÷ or divsion sign to be an equation