Using the binomial distribution, it is found that:
a) There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
b) There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
c) The probability is higher than 5%, so it would not be unusual.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
Sample of 12, thus [tex]n = 12[/tex]0.267 probability that a person covers their mouth, thus [tex]p = 0.27[/tex].Item a:
This probability is P(X = 7), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{12,7}.(0.267)^{7}.(0.733)^{5} = 0.0162[/tex]
There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
Item b:
The probability is P(X < 4), which is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.267)^{0}.(0.733)^{12} = 0.0241[/tex]
[tex]P(X = 1) = C_{12,1}.(0.267)^{1}.(0.733)^{11} = 0.1052[/tex]
[tex]P(X = 2) = C_{12,2}.(0.267)^{2}.(0.733)^{10} = 0.2107[/tex]
[tex]P(X = 3) = C_{12,3}.(0.267)^{3}.(0.733)^{9} = 0.2558[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0241 + 0.1052 + 0.2107 + 0.2558 = 0.5958[/tex]
There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
Item c:
This probability is:
[tex]P(X < 6) = P(X < 4) + P(X = 5) = 0.5958 + P(X = 5)[/tex]
Negative probabilities do no exist, thus, this probability is guaranteed to be above 0.05, which means that it would not be unusual if fewer than half covered their mouth when sneezing.
A similar problem is given at https://brainly.com/question/24923631
Simplify x ^8/ x ^6
Answer:
[tex]\displaystyle \frac{x^8}{x^6} = x^2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Property [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{x^8}{x^6}[/tex]
Step 2: Simplify
Exponential Rule [Dividing]: [tex]\displaystyle \frac{x^8}{x^6} = x^{8 - 6}[/tex][Exponents] Subtract: [tex]\displaystyle \frac{x^8}{x^6} = x^{2}[/tex]Find the distance between each pair of points.
(-2,-3), (8,-1)
How do I find the difference? Due today!
I HOPE IT WILL HELP YOU.
Thank you.
Answer two questions about Equations
A
AA and
B
BB:
A
.
3
(
x
+
2
)
=
18
B
.
x
+
2
=
18
A.
B.
3(x+2)
x+2
=18
=18
1) How can we get Equation
B
BB from Equation
A
AA?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Multiply/divide both sides by the same non-zero constant
(Choice B)
B
Multiply/divide only one side by a non-zero constant
(Choice C)
C
Rewrite one side (or both) by combining like terms
(Choice D)
D
Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answer:
choice B is the answer be cause you're only dividing one side by 3
and no because if you actually solve both equations separately, the answers are not the same
51661-61661+611×5561×58
Solve.
Answer:
=197060718
Step-by-step explanation:
51661−61661+(611)(5561)(58)
=−10000+(611)(5561)(58)
=−10000+(3397771)(58)
=−10000+197070718
=197060718
In your own words, how important is your knowledge of solving real-life problems involving
inverse functions?
what the example of constant and variable?
Answer:
A constant is a defined value often portrayed as a number.
A variable is a value that can change and is often represented as a letter.
Step-by-step explanation:
For example:
In the equation ? = 10x + 3y + 17
10, 3, and 17 are all constants.
X and Y are both variables.
To reiterate, constants are known values that can NOT change while variables are unknown values that can change!
solve pls brainliest
The Answers
1. -2.65
2. 5.128
Answer:
-2.65
5.128
Step-by-step explanation:
-5.3*0.5 = -2.65
-512.8(-0.01)
-512.8 * -0.01 = 5.128
(two negatives multiplied cancel out to create a positive)
(sorry for login question pls help )
Fit Data to a line
When using empirical data ( data and information collected by scientists in an experiment ), sometimes, that data will not form a perfect line on a graph. when this happens, the line that is created using a linear regression is known as the " line of best fit " the following speed data was collected from a car moving with a constant acceleration.
1 - what is the line of best fit for this data? perform a linear regression on this table to find the equation .
2 - based on your equation, what was the car's approximate initial velocity (at time = 0) ?
3 - if the car continued at the same acceleration (meaning the slope of the line does not change), how fast would it be going in 15 seconds ?
Using a linear regression calculator, the best fit line, initial velocity and the velocity of the car after 15 seconds is :
y = 3.64x + 5.7 Initial Velocity = 5.7 m/s Velocity after 15 seconds = 60.3 m/sUsing technology, the linear regression equation obtained by fitting the data is :
y = 3.64x + 5.7x = times(seconds) ; y = velocity(m/s)The approximate velocity at time = 0 ; x = 0 :
y = 3.64(0) + 5.7
y = 0 + 5.7
y = 5.7 m/s
3.) Velocity after 15 seconds :
At time, x = 15 seconds
y = 3.64(15) + 5.7
y = 60.3 m/s
Therefore, the velocity of the car after 15 seconds is 60.3 m/s
Learn more :https://brainly.com/question/18405415
The formula for simple interest is I=Prt,I=Prt, where II is the interest earned, PP is the principal, rr is the interest rate and tt is the number of years. Solve the formula for tt in terms of P,P, II and r.r.
Answer:
t = I/pr
Step-by-step explanation:
I = prt
divide both sides by pr
i/pr = prt/pr , pr cancel out
I/pr = t
t = I/pr
Which system of linear inequalities is represented by
the graph?
HELPPP Please!!!
what is the math pattern
find x and y ILL GIVE BRAINLIESTTTT
Answer:
y =90° x =70°
Step-by-step explanation:
Answer:
x = 70° , opposite angles of the same line with angle 70.
sum of interior angles of trapezium is 360°.
y + 70° + 90° + 110° = 360°
y = 90°
5t+8=43
Pleas some one explain I do not understand.
Answer:
7
Step-by-step explanation:
5 times 7 is 35.
35 plus 8 is 43.
Yael worked out at a gym for 3 hours. Her workout consisted of stretching for 21
minutes, jogging for 39 minutes, and lifting weights for the remaining amount of
time. What percentage of Yael's workout was spent lifting weights?
21 + 39 = 60 minutes ( 1 hour)
So for the remaining time she lifted weights for about 2 hours.
3 hours = 180 minutes
180 - 60 = 120
About 66% of the remaining time Yael used to lift weights.
To be accurate 66.6% ( the last 6 repeating a infinite amount of time aka it doesnt end)
If the sides of a square measure 9units, then find the length of the diagonal.
Answer:
12.72792
Step-by-step explanation:
d = √2a = √2 x 9 = 12.72792
Sorry, I don't have too much time to explain the question but I hope this helps!
81a^2x+9a^2y-90bx-10by
I need help with #4 and #5
Answer:
Step-by-step explanation:
Help help help help pleaE
12.A T.V. is sold for Rs. 17,280 at a profit of 20%. Find the cost price of the T.V.
Answer:
Rs. 13,824
Step-by-step explanation:
20% of Rs. 17,280
= Rs.3456
Rs.17,280- Rs.3456
=Rs.13,824
Answer:
14400
Step-by-step explanation:
If 120%=17280
.100%=??
100%×17280/120
=1440×10=14400
Fresh and easy breath lozenges have only two 3/4 cal piece how many calories are in a pack of 16 lozenges
Select the correct statement in the table.
Given that r and s are both irrational numbers, determine which statement is true.
Answer:
Below.
Step-by-step explanation:
The value of r + x is always irrational.
The value of r. s is sometimes irrational:
- for example √2 * √3 = √6 which is irrational,
but √3 * √3 = √9 = 3 which is rational.
93 divided by 5932 long division
Answer:
63 73/93 (steps are in the attached file)
Step-by-step explanation:
4. The length of a rectangle is 2 centimeters less than twice its width (w) What is its
width if its perimeter is 50 centimeters
Answer:
This is math
Step-by-step explanation:
Answer:
width=9cm
Step-by-step explanation:
length=16cm
what are your recommendations about augmented learning
Answer:
Augmented learning is an on-demand learning technique where the environment adapts to the learner. By providing remediation on-demand, learners can gain greater understanding of a topic and stimulate discovery and learning.
Augmented learning is closely related to augmented intelligence and intelligence amplification.
Augmented learning is an on-demand learning technique where the environment adapts to the learner. By providing remediation on-demand, learners can gain greater understanding of a topic and stimulate discovery and learning.
Hope this helps you
HELPPPPPPPPPPPPPPPPPPPPPPP
Simplify the following square rots.When necessary, write the square root using the “WIRIS editor” button;
Answer:
[tex]3\sqrt{9}[/tex]
Step-by-step explanation:
[tex]\sqrt{ab}= \sqrt{a} *\sqrt{b}\\\\\sqrt{99}=\sqrt{9*11}\\\\=\sqrt{9}*\sqrt{11}\\=3\sqrt{11}[/tex]
a
Conduct a simulation using a random number generator based on the following information.
According to a survey by a restaurateur's magazine on favorite types of food, 45% of their
readers chose Italian, 25% Mexican, 15% American, 10% French, and 5% Ethnic.
Any number chosen randomly without any design or process is called a random number.
Italian, = 9/20
Mexican, = 5/20
American, = 3/20
French, = 2/20
and
Ethnic, 1/20
Suppose we choose as the random number then according to the given data
Italian,45% = 45/100 = 9/20
Mexican, 25% =25/100= 1/4× 5/5= 5/20
American, 15% = 15/100= 3/20
French, 10% = 10/100 = 1/10 = 2/20
and
Ethnic, 5% = 5/100 = 1/20
If we add the fractions it sums up to 1 which shows their true probability.
The sum of probability can never be greater than 1 . It is always equal to 1.
https://brainly.com/question/10292453
https://brainly.com/question/16802829
irreducible fraction of -30/40
Answer:
-3/4
Step-by-step explanation:
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered).
so
-30/40 =
-3/4
PLEASE SHOW STEPS // -5 (2b + 7) + b < -b - 11
Answer:
b < -11
Step-by-step explanation:
-5 X 2b = -10b + -35 +b
-10b + 35 + b < -b -11
-b -b
cancel out the b
-10b + 35 < -11
-35 < - 35
-10b <-11
-10 < -10
b < -11 and that's your answer
what is 7 times zero and eight tenths
Answer: 5.6
Step-by-step explanation:
8x7=56
Move the decimal from 56 once to the left because there is 1 number behind the decimal.