According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a) What is the probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing?
(b) What is the probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? Why?
Answers
Using the binomial distribution, it is found that:
a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
What is the binomial distribution formula?The formula is:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 18, p = 0.267.
Item a:
The probability is P(X = 6), hence:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 6) = C_{18,6}.(0.267)^{6}.(0.733)^{12} = 0.1618\)
There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
Item b:
The probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{18,0}.(0.267)^{0}.(0.733)^{18} = 0.0037\)
\(P(X = 1) = C_{18,1}.(0.267)^{1}.(0.733)^{17} = 0.0245\)
\(P(X = 2) = C_{18,2}.(0.267)^{2}.(0.733)^{16} = 0.0758\)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.
There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
item c:
We have to look at the mean and the standard deviation, given, respectively, by:
E(X) = np = 18 x 0.267 = 4.81.\(\sqrt{V(X)} = \sqrt{18(0.267)(0.733)} = 1.88\)9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
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Related Questions
Which equation represents a nonlinear
Function
2y = 1/2x + 5
y = 1/2x - 5
3y = 1/2x + 5
4y = (1/2)^x -5
Answers
Answer:
4y = (1/2)^x -5
Step-by-step explanation:
The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!
You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!
The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.
If a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.
Answers
Answer:
The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:
standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7
To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:
z = (37.4 - 40) / (8 / 7) = -1.225
Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.
give thanks, your welcome <3
Step-by-step explanation:
Solve by graphing. x2 + 2x – 3 = 0
Answers
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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I need help with This question no links or I will report you
Answers
Answer:
Below.
Step-by-step explanation:
So let's do this Divide both sides.
equals to,
y+2>2
Cancel out equal terms.
y>0.
Write the polynomial in factored form as a product of linear factors:
p(a) = a^3 + 3a^2+ 9a + 27
zeros of polynomial.
Answers
Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?
Answers
Answer:
9
Step-by-step explanation:
What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.
We can now use a proportion to find the value of w.
\(\frac{4}{3} = \frac{12}{x}\)
Cross multiply:
\(12\cdot36 = 36\\\\36\div4=9\)
Hope this helped!
Answer: 9
Step-by-step explanation:
Pls help I’ll brainlest
Answers
Answer:
30.5 feet / minute
Step-by-step explanation:
Rate of descent is the same as speed (of falling). The formula for speed is distance / time = speed
First, find how much it fell.
4595 - 3131 = 1464 feet
Divide the distance by the time.
1464 feet / 48 minutes = 30.5 feet / minute
What’s the correct answer for the question??
Answers
Answer:
i dont get this im really sorry but it just doesnt make any sence at all
Step-by-step explanation:
Let y represent any number in this sequence.1, 5, 25, 125,Which of these can be used to determine the next number in this sequence?5yy/5y+4
Answers
we have
\(undefined\)When Brooklyn commutes to work, the amount of time it takes he
normally distributed with a mean of 54 minutes and a standard deviation of 4
minutes. Using the empirical rule, what percentage of her commutes will be between
50 and 58 minutes?
Answers
Answer:
Step-by-step explanation:
68
The percentage of her commutes will be between 50 and 58 minutes is 68%.
What Is an Empirical Rule in Statistics?The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule that states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
Given: mean=54, standard deviation =4 min
The Empirical says,
mean-standard deviation= 54-4=50
mean - standard deviation= 54+4= 58.
Now,
P(\(\mu\)-6 ≤ X ≤ \(\mu\) +6) ≈0.68
Hence, percentage of her commutes will be between 50 and 58 minutes is 68%.
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Among employees of a certain company, 60% know C/C++, 50% know R, 30% know both languages, and 20% know neither language. Let A = "knows C/C++" and B = "knows R". What is the probability that a randomly chosen employee knows C/C++ or they know R? Answer should be in decimal form.
Answers
The probability that the randomly chosen employee knows C/C++ or R will be 0.30.
What is probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
Probability and odds are two distinct ideas.
Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.
So, employees who know C/C++ are 60%.
Which will be: 60/100
Employees who know R are 50%.
That will be 50/100.
The probability that a randomly chosen employee knows C/C++ or R:
60/100 * 50/100
6/10 * 5/10
30/100
0.30
Therefore, the probability that the randomly chosen employee knows C/C++ or R will be 0.30.
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Museums offer programs, such as Friday night gatherings or hand-on art activities, to draw the public into the museum in hopes of
enticing them to visit frequently.
true or false
Answers
Answer:
False
Step-by-step explanation:
That's Maths? False though
4x=2y-9 plus -8x+6y=6
Answers
Answer:
-4x+4y+3=0
Step-by-step explanation:
(4x-2y+9=0)+(-8x+6y-6=0)
Add like terms:
-4x+4y+3=0
24. This week, Cristina eamed P594.65 from selling burgers for 35 days. How much he will earn in 5 days?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter. You got 88.75 for the first quiz, 85.5, 90.5, and 87.25 in the second, third and fourth quizzes, respectively. What is your average in the four quizzes this quarter?
A. 86.5
B. 88
C. 89.5
D. 90 26. Amberich put P580.00 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for one year in pesos and centavos?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
24. This week , Cristina eamed P594.65 from selling burgers for 35 days . How much he will earn in 5 days ?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter . You got 88.75 for the first quiz , 85.5 , 90.5 , and 87.25 in the second , third and fourth quizzes , respectively . What is your average in the four quizzes this quarter ?
A. 86.5
B. 88
C. 89.5
D. 90
26. Amberich put P580.00 into a savings account for one year . The rate of interest on the account was 6.5 % . How much was the interest for one year in pesos and centavos ?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
Answers
Question 24 :
P594.65 : 35 days
P594.65/7 : 35/7 days
P84.95 : 5 days
⇒ A. P84.95
Question 25 :
88.75 + 85.5 + 90.5 + 87.25 / 4
352/4
88
⇒ B. 88
Question 26 :
I = P × r × t
I = 580.00 × 0.065 × 1
I = P37.70
⇒ B. P37.70
If there are 10 miles already driven and the gasoline left is 8.5 with a y-intercept of 9. What is the slope?
Answers
The slope between the parameters of the amount of gasoline is 0.12
How to determine the slope?The given parameters are
10 miles already driven and the gasoline left is 8.5y-intercept of 9.The above parameters can be represented as
(x, y) = (0, 9) and (8.5, 10)
The slope between the points is calculated as
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
So, we have
m = (10 - 9)/(8.5 - 0)
Evaluate the difference in the above equation
So, we have
m = 1/8.5
Evaluate the quotient in the above equation
So, we have
m = 0.12
Hence, the slope between the parameters is 0.12
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In right triangle ABC, 2
Answers
Answer:
here your answer
sorry if wrong
In permutations, order matters.
A) True
B) False
C) Both
D) Unable to answer this question with the data given because permutations are always changing.
Answers
Need help with B Just simplifying surds please help!!!!!!
Answers
I HOPE IT WILL HELP YOU.
Thank you.
^ - ^
Answer:
12
Step-by-step explanation:
Sqrt 8 x sqrt 18 = sqrt (8 x 18)
= sqrt 144 = 12
Irene y Alejandro tienen 73 libros irene tiene el doble que Alejandro mas 1 cuantos libros tiene cada uno?
Answers
Irene has 49 Books, and Alejandro has 24 books.
Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:
1. Irene has twice as many books as Alejandro plus 1:
x = 2y + 1
2. The total number of books between Irene and Alejandro is 73:
x + y = 73
We can now solve this system of equations to find the values of x and y.
Substituting the value of x from equation (1) into equation (2), we have:
(2y + 1) + y = 73
3y + 1 = 73
3y = 72
y = 24
Now, we can substitute the value of y into equation (1) to find x:
x = 2(24) + 1
x = 49
Therefore, Irene has 49 books, and Alejandro has 24 books.
To verify our solution, we can check if the sum of their books equals 73:
49 + 24 = 7
So, our solution is correct.
In conclusion, Irene has 49 books, and Alejandro has 24 books.
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If tan x° = 6 divided by g and sin x° = 6 divided by h, what is the value of cos x°?
Answers
Answer:
adjacent / hypotenuse cos x° = g divided by h is right
Step-by-step explanation:
If \(tanx^{o} = \frac{6}{g}\) and \(sinx^{o} = \frac{6}{h}\) then \(cosx^{o} = \frac{g}{h}\) .
Trigonometric Ratios:By right angled triangle we have,
Trigonometric ratios as
sinθ = \(\frac{opposite}{hypotenuse}\) cosθ = \(\frac{adjacent}{hypotenuse}\)tanθ = \(\frac{opposite}{adjacent}\)Given \(sinx^{o} = \frac{6}{h}\) and \(tanx^{o} = \frac{6}{g}\)
By comparison, we haveopposite = 6, hypotenuse = h, adjacent = g
Hence, we can write\(cosx^{o}\) = \(\frac{adjacent}{hypotenuse}\) \(=\frac{g}{h}\)
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Sam and Bethan share £54 in the ratio 5:4 how much does each person get
Answers
Answer:add 5 and 4, you get 9. divide 54 by 9, and you get 6. this is because for every 5 sam gets bethan will get 4. if you add, that, you will get the total amount for 1 share.
Step-by-step explanation:
Answer:
Sam gets £30
Bethan gets £24
Step-by-step explanation:
Since they split the money in a ratio of 5:4, that means for every 5 parts of the money that Sam gets, Bethan gets 4 parts. The total of 5 parts and 4 parts is 9 parts.
To find how much each part is, we divide £54 by 9.
£54/9 = £6
Each part is £6.
Sam gets 5 parts: 5 × £6 = £30
Bethan gets 4 parts: 4 × £6 = £24
find the sum of all the integers from 1 to 1000
Answers
Answer:
500500
Step-by-step explanation:
intergers are whole numbers which are not fractions
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answers
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x4what is the √-1 please under complex numbers
Answers
Imaginary number (i'm serious, that's what it's called i'm not trying to be funny)
Answer:
i is the answer
Step-by-step explanation:
When using complex numbers you take the square root of negative one as i
for example: If I have √-16 I need to take √-1 out first and then put i in for √-1. Therefore my answer would be i√16
i = imagiary number aka √-1
In your case the answer is i
I hope this helped you!!
I did this for Algebra 2 on FLVS and got a 100%
Point A is on a number line halfway between -17 and 5. Point B is halfway between point A and 0. What integer does point B reprsent?
Answers
Point B: (－6＋0)÷2=－3
Hope my answer helped u :)
please
\(2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 \)
I need help
Answers
![please [tex]2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 [/tex]I need help](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/0X88LdBuMwIAUWxByc8exEH7JSTCTQBj.png)
An equation is shown below: 5(3x − 15) + 16 = 5x + 11 Part A: Write the steps you will use to solve the equation, and explain each step. (8 points) Part B: What value of x makes the equation true? (2 points)
Answers
The result of the unknown variable x is equivalent to 7
Solving linear equationsLinear equations are equation that has a leading degree of 1. Given the expression below:
5(3x − 15) + 16 = 5x + 11
Expand the expression
5(3x) - 5(15) + 16 = 5x + 11
15x - 75 + 16 = 5x + 11
15x - 5x - 59 - 11 = 0
10x - 70 = 0
10x = 70
Divide both sides by 10
10x/10 = 70/10
x = 7
Hence the value of x makes the equation true is 7
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before soccer practice. Laura warms up jogging around the rectangular soccer field that is 80 yards by 120 yards how many yards does she jog if she goes around the field 2 times
Answers
Answer:
The answer is 19200
Step-by-step explanation:
120x80=9600×2=19200
X
Y
If L=4, Y=30 and Z=14. Solve for X. (round to 2 decimal places)
L
N
Answers
Answer:
Y+Z/Z = X/L
X= (44/14)4 = 12.57(nearest 2 decimal
packaging idaho produce company ships potatoes to its distributors in bags whose weights are normally distributed witb. nean weight of 50 pounds and a standard deviation of .5 pounds. if a bag of potatoes is selected at random from a shipment, what is the probability that it weighs more than 51 pounds
Answers
The probability that it weighs more than 51 pounds exactly 53 pounds.
Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.
We need to find the probability that it weighs more than 51 pounds,
P(X = 53) = 0
z = (51 - 50) / 0.5 = 2.00
P(X > 51) = P(z > 2.00) = 0.0228
z1 = (49 - 50) / 0.5 = -2.00
z2 = (51 - 50) / 0.5 = 2.00
P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544
Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.
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