Every person in a group of 1000 people has a 1% chance of being infected by a virus. The process of being infected is independent from person to person. Using random variables, write expressions for the following probabilities and solve them with R(a) The probability that exactly 10 people are infected
Solution:
a)Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X = 10) = dbinom {1000}{10} $ $(0.01)^{10}$ $(1-0.01)^{990}
Using R, the expression for the probability that exactly 10 people are infected is:
p1 <- dbinom(10, 1000, 0.01)Ans: p1
(b) That probability that at least 16 people are infected.
Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - $\sum\limits_{i=0}^{15}$ $ \dbinom {1000}{i} $ $(0.01)^i$ $(1-0.01)^{1000-i}$Using R, the expression for the probability that at least 16 people are infected is:
p2 <- 1-pbinom(15, 1000, 0.01)Ans: p2
c) The probability that between 12 and 14 people are infected
.Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01
. Then, P(12 ≤ X ≤ 14) = $\sum\limits_{i=12}^{14}$ $ \dbinom {1000}{i} $ $(0.01)^i$ $(1-0.01)^{1000-i}$Using R, the expression for the probability that between 12 and 14 people are infected is:
p3 <- sum(dbinom(12:14, 1000, 0.01))Ans: p3
d) The probability that someone is infected
.Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X ≥ 1) = 1 - P(X = 0) = 1 - $ \dbinom {1000}{0} $ $(0.01)^0$ $(1-0.01)^{1000-0}$Using R, the expression for the probability that someone is infected is:
p4 <- 1-dbinom(0, 1000, 0.01)Ans: p4
To know more about binomial distribution:
https://brainly.com/question/31197941
#SPJ11
suppose that the cumulative probability of a company defaulting by years one, two, three and four are 3%, 6.5%, 10%, and 14.5%, respectively. what is the probability of default in the fourth year conditional on no earlier default?
The probability of default in the fourth year conditional on no earlier default is 14.5%. Option (4).
The probability of default in the fourth year conditional on no earlier default is equal to the probability of default in the fourth year, given that the company did not default in the first three years.
Using the conditional probability formula, we can calculate this probability as follows:
P(Default in Year 4 | No earlier default) = P(Default in Year 4 and No earlier default) / P(No earlier default)
We can calculate the numerator by multiplying the probability of default in the fourth year (14.5%) by the probability of no earlier default, which is the complement of the sum of the probabilities of default in the first three years:
P(Default in Year 4 and No earlier default) = 0.145 x (1 - 0.03 - 0.065 - 0.10) = 0.145 x 0.705 = 0.102
The denominator is simply the probability of no earlier default, which we just calculated:
P(No earlier default) = 1 - 0.03 - 0.065 - 0.10 = 0.705
Now we can substitute these values into the conditional probability formula:
P(Default in Year 4 | No earlier default) = 0.102 / 0.705 = 0.1449, or approximately 14.5%
Therefore, the probability of default in the fourth year conditional on no earlier default is 14.5%.
Learn more about probability
https://brainly.com/question/30034780
#SPJ4
Full Question : Suppose that the cumulative probability of a company defaulting by years one, two, three and four are
3%, 6.5%, 10%, 14.5%,respectively. what is the probability of default in the fourth year conditional on no earlier default?
Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 1/5 + x f(x) = sigma^infinity_n = 0 ((1/5 + x)^n) Determine the interval of convergence.
a) The power series representation of f(x) = 1/5 + x f(x) centered at x = 0 is f(x) = sigma^infinity_n = 0 ((x/5)^n)
b) The interval of convergence is (-5, 5)
To find the power series representation of f(x), we can use the formula for the geometric series
1 / (1 - r) = sigma^infinity_n = 0 (r^n)
where r is a constant.
In this case, we have
f(x) = 1/5 + x f(x)
We can solve for f(x) to get
f(x) = 1/5 / (1 - x)
Using the formula for the geometric series with r = x/5, we have
f(x) = sigma^infinity_n = 0 ((x/5)^n)
Multiplying both sides by 5, we get
5f(x) = sigma^infinity_n = 0 (x^n
So the power series representation of f(x) centered at x = 0 is
f(x) = sigma^infinity_n = 0 ((x/5)^n)
To determine the interval of convergence, we can use the ratio test
| (x/5)^(n+1) | / | (x/5)^n | = |x/5|
The series converges if the limit of |x/5| as n approaches infinity is less than 1. This is true when |x| < 5, so the interval of convergence is (-5, 5).
Learn more about power series here
brainly.com/question/17193241
#SPJ4
You're playing a game in which the probability of winning each round is. 20.
On average, how many rounds do you have to play to first win?
Answer: You would probably have to play about 10 rounds.
if you consume seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?
The probability of consuming at least one insect fragment in more than one bar is 0.3011.
Given that you consumed seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level. The probability of finding one or more insect fragments in a 28.35-gram chocolate bar that is produced with the mean level of contamination is 0.4875.
The probability that you consume one or more insect fragments in a single bar is 0.4875The probability that you will not consume an insect fragment in a single bar is 0.5125
The probability that you will not consume an insect fragment in any of the seven bars is 0.5125⁷ = 0.0236The probability that you consume one or more insect fragments in more than one bar is 1 - 0.0236 = 0.9764The probability that you consume one or more insect fragments in more than one bar is 0.9764.
The probability that you consume one or more insect fragments in more than one bar is 0.3011.
To know more about probability refer here:
https://brainly.com/question/1596693#
#SPJ11
question sebastian states that experimental and theoretical probabilities are never the same. is sebastian's statement true? why or why not?
Answer:
Step-by-step explanation:
yes
Consider parallelogram ABCD below. Point E is the intersection of diagonals AC and BD.
Progress: 0/2
Part 1 of 2
4(-2,2)
D(-2,-10)
(a) Find the area of AABE.
cm
2
B (8.2)
C(8.-10)
HELP ASAP ON TIME LIMIT 50 PNTS
Answer:
A:1,142 miles.
B; 187.30
C; 4
Write a word sentence for the question
x - 14 = 52
Answer:
under quadratic equation of fatorisation
A function is shown on the coordinate plane below. For what intervals is the function increasing?
pls hurry
The function is increasing over the intervals D. -6 < x < -1 and 2 < x < 3 and 4 < x < 6.
When does a function increase?A function is increasing when the slope of its graph is positive, meaning that its graph is rising from left to right.
In the given coordinate plane, the graph of the function consists of three sections, each of which has an increasing slope.
The first section is from -6 to -1, the second section is from 2 to 3, and the third section is from 4 to 6.
This means that the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6.
To confirm this, we can calculate the slope of the graph in each interval. The slope of the graph between two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1).
For the first interval, the slope is (3-(-5))/(-1-(-6)) = 8/-5 = -1.6. This is a negative value, which means the graph is decreasing over this interval. For the second interval, the slope is (4-3)/(3-2) = 1/1 = 1. This is a positive value, so the graph is increasing over this interval.
For the third interval, the slope is (6-4)/(4-2) = 2/2 = 1. This is also a positive value, so the graph is increasing over this interval as well.
Therefore, the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6, which is option D.
For more questions related to slope
https://brainly.com/question/3493733
#SPJ1
Which of the following is not a correct comparison among the Z-distribution and all the t-distributions? Group of answer choices
A. They have the same mean.
B. They have the same unusual features.
C. They have the same standard deviation.
D. They have the same shape
E. They have the same shape.
Among the following, "They have the same unusual features" is not a correct comparison among the Z-distribution and all the t-distributions. Option B is the correct answer.
A z-distribution refers to the normal distribution of a standard set of values for a variable. If a variable has a normal distribution with a mean of 0 and a standard deviation of 1, it is said to follow a standard normal distribution, which is also known as a z-distribution.
A t-distribution is a type of probability distribution that is used in statistical analysis when the sample size is small or the population's standard deviation is unknown. T-distributions are used in a variety of statistical tests, including the t-test and the analysis of variance (ANOVA). T-distributions are a family of distributions that resemble the normal distribution, with the tails stretched to either side, based on the number of degrees of freedom.
In general, the t-distribution is less peaked and has heavier tails than the normal distribution. As the degrees of freedom increase, the t-distribution approaches the normal distribution. Thus, Option B "They have the same unusual features" is not a correct comparison among the Z-distribution and all the t-distributions.
You can learn more about t-distributions at
https://brainly.com/question/17469144
#SPJ11
how many vectors may be added by the polygon method? are other methods of vector addition limited to the number of vectors that can be added? explain.
The polygon method of vector addition can be used to add any number of vectors. Other methods of vector addition, however, may be limited to the number of vectors that can be added.
The vector addition method known as the polygon method can be used to add any number of vectors. To use the polygon method, you simply place the vectors head to tail, as if constructing the sides of a polygon. The sum of the vectors is then the vector from the tail of the first vector to the head of the final vector. Polygon method of vector additionIn addition, other methods of vector addition, such as the component method, may have limits on the number of vectors that can be added. When using the component method, for example, vectors are broken down into their x- and y-components.
These components are then added to determine the total x- and y-components of the sum vector. The sum vector is then found by combining the x- and y-components. Because of this, the number of vectors that can be added using the component method may be limited by the ability to calculate the individual x- and y-components.
Learn more about The polygon method of vector addition:https://brainly.com/question/13264689
#SPJ11
Is 8 a reasonable solution to log(-x)=log(x-16)?
A) Yes, 8 is a reasonable solution because 8 is positive and -(8)=(8)-16
B) No, 8 is NOT a reasonable solution because at x=8, the logarithm is not defined.
The rate of consumption of C3H6 in the following reaction is 0.45 M/s. Calculate the rate of production of H2O. 2 C3H6 + 2 NH3 + 3 O2 rightarrow 2 CH2CHCN + 6 H2O
Answer:
The rate of production of H2O is 1.35 M/s.
Step-by-step explanation:
To calculate the rate of production of H2O, we need to consider the stoichiometry of the balanced chemical equation:
2 C3H6 + 2 NH3 + 3 O2 → 2 CH2CHCN + 6 H2O
Given the rate of consumption of C3H6 is 0.45 M/s, we can use the mole ratio between C3H6 and H2O to find the rate of production of H2O.
Step 1: Determine the mole ratio of C3H6 to H2O in the balanced equation.
Mole ratio = (moles of H2O produced) / (moles of C3H6 consumed) = 6 / 2 = 3
Step 2: Calculate the rate of production of H2O.
Rate of H2O production = (rate of C3H6 consumption) × (mole ratio) = 0.45 M/s × 3 = 1.35 M/s
So, the rate of production of H2O is 1.35 M/s.
Learn more about rate of production of H2O,
https://brainly.com/question/29121165
#SPJ11
There is an amoeba (a single-celled animal) on a dish.
After one hour, the amoeba divides to form two amoebas.
One hour later, each amoeba divides to form two more.
Every hour, each amoeba divides to form two more.
Why might exponential notation, like `2^{6}`, be useful for answering these questions?
Exponential notation is useful in this scenario because it can help us quickly calculate the total number of amoebas that exist after a certain number of hours without having to write out each step of the division process.
What is exponential notation?Exponential notation, also known as scientific notation, is a way of representing a number as a product of two factors: a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 indicates how many places the decimal point must be moved to obtain the original number.
In the given scenario, we can see that each amoeba doubles every hour, which is an example of exponential growth. Using exponential notation, we can represent the number of amoebas after n hours as 2^n. For example, after 2 hours, there would be 2^2 = 4 amoebas, and after 3 hours, there would be 2^3 = 8 amoebas.
Learn about exponential notations here https://brainly.com/question/30239895
#SPJ1
a rectangle has a length of 25 cm and a width of 12.25 cm. a larger, similar rectangle has a width 49 cm. what is the length of the larger rectangle?
Answer: 100 cm
Step-by-step explanation:
1. Since the problem tells us that they are similar, we can infer that this larger rectangle is the same rectangle, only bigger.
2. With this information, we can do the equation 49/12.25 because then we will get the amount the rectangle grows by.
3. 49/12.25=4
4. Now, we can multiply the length(25) by 4.
5. 25 x 4=100
6. The length of the larger rectangle is 100.
I hope this helps!
find the perimeter. x+10y units 4x^2-x+9y units
The perimeter of the rectangle is equal to (8x² + 38) units.
Perimeter of rectangleThe perimeter of a rectangle is the sum of length of its four sides or the sum of its length and breadth, multiplied by two.
length = (4x² - x + 9y) units
breadth = (x + 10y) units
perimeter = 2×(length + breadth)
perimeter of the rectangle = 2(4x² - x + 9y + x + 10y) units
perimeter of the rectangle = 2(4x² + x - x + 9y + 10y) units
perimeter of the rectangle = 2(4x² + 19y) units
perimeter of the rectangle = (8x² + 38y) units
Therefore, the perimeter of the rectangle is equal to (8x² + 38) units.
Read more about rectangle here:https://brainly.com/question/17297081
#SPJ1
assuming a constant growth factor, by what percent did the population of gotham city grow each year? give at least 3 decimal places.
Assuming a constant growth factor, the population of Gotham City grew by approximately 4.287% each year.
This can be calculated using the formula for exponential growth, which is:
y = a * (1 + r)^t
Where: y = final value of the population
a = initial value of the population
r = annual growth rate expressed as a decimal
t = number of years
For this problem, let's assume that the initial population of Gotham City was 100,000 and that the population grew for 10 years.
Using these values, we can calculate the annual growth rate as follows:
100,000 * (1 + r)^10 = final population
r = (final population / 100,000)^(1/10) - 1
Plugging in a final population of 148,644 (which is a 48.644% increase from the initial population),
r = (148,644 / 100,000)^(1/10) - 1r = 0.04287 (rounded to 5 decimal places)
Therefore, the annual growth rate (or percentage increase) is approximately 4.287% (rounded to 3 decimal places).
To know more about growth rate refer here:
https://brainly.com/question/13870574
#SPJ11
in how many ways can 4 children be arranged on a 4-animal merry go round if andy is seated on the giraffe
There are 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.
If Andy is seated on the giraffe in a 4-animal merry-go-round, the arrangement of four children on the merry-go-round can be determined as follows:
Since Andy is already seated on the giraffe, only three children are left to be seated on three other animals. The first child can be seated on any of the three remaining animals. The second child can be seated on either of the two remaining animals since one has already been occupied.
Finally, the third child can be seated on the only remaining animal. Therefore, there are three options for the first child, two options for the second child, and one option for the third child, resulting in 3*2*1 = 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.Answer:6.
Learn more about permutation theory:https://brainly.com/question/12468032
#SPJ11
What is the value of letter D on the number line?
Answer:
What is the value of the letter D on the number line?
Three and twenty-five hundredthsStep-by-step explanation:
You're welcome
Prove that 3:8 is equivalent to 12:32
Answer:
3:8 = 12:32
For easier understanding, we make 3:8 into 3/8 and 12:32 into 12/32
3/8 = 12/32
Cross multiply
3*32 = 8*12
96 = 96
Since the products are equal, the ratios are equivalent.
You can also simplify 12:32
12 / 4 = 3
32 / 4 = 8
Help me!!! please show working out
The polynomial x² + x - 4 = 0 is equivalent to the rational equation [2 · (x + 2) - (x + 1)] / [(x + 1) · (x + 2)] = 1 / 2.
How to find the equivalent polynomial related to rational equation
In this problem we find the definition of a rational equation that must transformed into an equivalent polynomial. This can be done by using algebra properties:
2 / (x + 1) - 1 / (x + 2) = 1 / 2
First, use subtraction between fractions of different denominators:
[2 · (x + 2) - (x + 1)] / [(x + 1) · (x + 2)] = 1 / 2
(2 · x + 4 - x - 1) / (x² + 3 · x + 2) = 1 / 2
(x + 3) / (x² + 3 · x + 2) = 1 / 2
Second, eliminate the denominator on both sides:
2 · (x + 3) = x² + 3 · x + 2
2 · x + 6 = x² + 3 · x + 2
x² + x - 4 = 0
To learn more on rational equations: https://brainly.com/question/31057486
#SPJ1
if you flip two coins 28 times, what is the best prediction possible for the number of times both coins will land on heads?
When you flip two coins 28 times, the best prediction possible for the number of times both coins will land on heads is 7 times.
This can be explained with the following calculations:
When flipping a coin, the chance of getting heads or tails is 1/2 or 0.5.
If you flip two coins, the probability of getting two heads is calculated by multiplying the probability of getting heads on the first coin by the probability of getting heads on the second coin, which is (1/2) x (1/2) = 1/4 or 0.25 or 25%.
To calculate the expected number of times both coins will land on heads in 28 flips, we use the following formula:
Expected value = Probability x Total number of flips
Expected value = 0.25 x 28
Expected value = 7
Therefore, the best prediction possible for the number of times both coins will land on heads is 7 times.
It's important to note that this is only a prediction, and the actual number of times both coins land on heads could be more or less than 7.
This is because probabilities are based on chance, and chance outcomes can be unpredictable.
For similar question on probability.
https://brainly.com/question/29061226
#SPJ11
Solve the following quadratic equations by factoring
Answer:
x=5 or x=-5
Step-by-step explanation:
[tex]x^{2} -25=0[/tex]
[tex](x-5)(x+5) =0[/tex]
[tex]x=-5 \\x=5[/tex]
Can someone help me with this?
I'm not sure how to execute this.
Anything helps! Will give brainliest!
Answer:
165 centimeters squared.
Step-by-step explanation:
Since we have 2 shapes combined, we need to split them to make 2 rectangles. Now that we have split these two, we can find their individual areas. We know the formula to find area is L * W = A.
So now we do 15 * 7 = 105 to find the area of the shape on the left.
To find the area of the shape on the right, we do 10 * 6 = 60.
Now we add these to get 165 centimeters squared.
Warm up State the theorems and show the steps needed to find the measure of angle a
Answer:
a=100
Step-by-step explanation:
The diagram shown is two intersecting lines. The measure of <5 is 42°.
Two intersecting lines. Not perpendicular. Angles labeled from far left counterclockwise are labeled 5 then 6 then 7
What is the measure of <7 ? How do you know. Explain your answer in complete sentences.
Suppose the measure of <6 can be represented by(3x-9). What equation can be written to solve for the value of x?
What is the value of x?
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
what is angle ?The distance between two intersecting lines or planes is measured in terms of angles. The amount of rotation required to align one of the lines or planes with the other is usually expressed in terms of degrees. The range of an angle is 0 degrees (i.e., no rotation) to 360 degrees (corresponding to a complete rotation).
given
As angles 5 and 7 are a pair of linear angles, their sum must be 180 degrees. Angle 7 therefore has a measure of 180 - 42 = 138 degrees.
We can use the fact that angles 6 and 7 are vertical angles and have the same measure to find the value of x. As a result, we can set the following phrase to indicate that the measure of angle 6 is equal to angle 7:
3x - 9 = 138
In order to find x, we add 9 to both sides and divide the result by 3:
3x = 147
x = 49
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
Darius wrote two integers on the chalkboard. The integers she wrote were 256 and -17. How much larger is 256 than -17?
Answer: 239
Step-by-step explanation:
Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger
Hope this helps
Answer: They are exactly 273 places away.
Step-by-step explanation:
If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.
Hope this helps!
Have a blessed day!
The tv had a volume 2808 the width measures 24 inches and the height measures 18 inches what is the depth of the tv?
Use translations to graph the given function.
Based on the graph, it looks like the function being graphed is h(x) = √(x+4).
To graph this function using translations, we can start by looking at the graph of the parent function f(x) = √x, which is a basic square root function. The graph of f(x) looks like a half of a parabola, opening up from the origin (0,0), and it includes all points with non-negative x-coordinates.
To graph h(x) = √(x+4), we can start by applying a horizontal shift to the graph of f(x) by replacing x with (x - (-4)) = (x + 4). This will shift the graph of f(x) to the left by 4 units. The resulting function is:
h(x) = √(x+4) = f(x+4)
Next, we can apply a vertical shift of 4 units up, which will move the entire graph of h(x) up by 4 units. The resulting function is:
h(x) = √(x+4) + 4
Using these translations, we can graph h(x) as follows:
Start with the graph of f(x) = √x.
Shift the graph to the left by 4 units by replacing x with (x+4).
Shift the graph up by 4 units by adding 4 to the function.
Plot some points on the resulting graph and connect them with a smooth curve.
The resulting graph should look like the one in the image you provided.
To learn more about function click here
brainly.com/question/30594198
#SPJ1
a pwr core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores
The probability of finding 10 defective cores in a sample of 10 power cores is approximately 0.0000161, or about 0.0016%.
Assuming that each fuel rod is independent of each other and that the probability of finding a defective fuel rod is constant at 0.1%, we can model the number of defective fuel rods in a power core with a binomial distribution. Let X be the number of defective fuel rods in one power core, then X follows a binomial distribution with parameters n = 50000 and p = 0.1/100 = 0.001.
To find the probability of finding 10 defective cores, we can use the binomial distribution again, but with a different set of parameters. Let Y be the number of defective cores in a sample of 10 power cores, then Y follows a binomial distribution with parameters n = 10 and p = P(X ≥ 1), where P(X ≥ 1) is the probability of finding at least one defective fuel rod in one power core. We can find P(X ≥ 1) using the complement rule:
P(X ≥ 1) = 1 - P(X = 0)
= 1 - (1 - 0.001)^50000
≈ 0.3935
So, the probability of finding 10 defective cores in a sample of 10 power cores is:
P(Y = 10) = (10 choose 10) * (0.3935)^10 * (1 - 0.3935)^(10 - 10)
≈ 0.0000161
Learn more about Probability at:
brainly.com/question/24756209
#SPJ4
Complete Question:
a power core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores.