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 . Suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) What is the probability that among randomly observed individuals exactly do not cover their mouth when sneezing? (b) What is the probability that among randomly observed individuals fewer than do not cover their mouth when sneezing? (c) Would you be surprised if, after observing individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly individuals do not cover their mouth is nothing. (Round to four decimal places as needed.) (b) The probability that fewer than individuals do not cover their mouth is nothing. (Round to four decimal places as needed.) (c) Fewer than half of individuals covering their mouth ▼ would would not be surprising because the probability of observing fewer than half covering their mouth when sneezing is nothing, which ▼ is is not an unusual event. (Round to four decimal places as needed.)
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(X = 8) = 0.0037[/tex]
b
[tex]P(X < 5) = 0.805[/tex]
c
[tex]P(X > 6) = 0.0206[/tex]
I would be surprised because the value is very small , less the 0.05
Step-by-step explanation:
From the question we are told that
The probability a randomly selected individual will not cover his or her mouth when sneezing is [tex]p = 0.267[/tex]
Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent
Hence for a randomly selected variable X we have that
[tex]X \ \ \~ \ \ { B ( p , n )}[/tex]
The probability distribution function for binomial distribution is
[tex]P(X = x ) = ^nC_x * p^x * (1 -p) ^{n-x}[/tex]
Considering question a
Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}[/tex]
Here C denotes combination
So
[tex]P(X = 8) = 495 * 0.000025828 * 0.28867947[/tex]
[tex]P(X = 8) = 0.0037[/tex]
Considering question b
Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)][/tex]
=> [tex]P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ][/tex]
=> [tex]P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964[/tex]
=> [tex]P(X < 5) = 0.805[/tex]
Considering question c
Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as
[tex]P(X > 6) = 1 - p(X \le 6)[/tex]
=> [tex]P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)][/tex]
=> [tex] P(X > 6)=1 - [^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 * (0.267)^6 * (1- 0.267)^{12-6} ][/tex]
=> [tex] P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ][/tex]
=> [tex]P(X > 6) = 0.0206[/tex]
I would be surprised because the value is very small , less the 0.05
(a )randomly observed individuals exactly do not cover their mouth when sneezing
[tex]P[x=8]=0.0037[/tex]
(b) randomly observed individuals fewer than do not cover their mouth when sneezing
[tex]P[x < 5]=0.805[/tex]
(c) fewer than half covered their mouth when sneezing
[tex]P(x > 6)=0.0206[/tex]
What will be the probability?It is given in the question that
The probability a randomly selected individual will not cover his or her mouth when sneezing is
[tex]P=0.267[/tex]
Generally, data collected from this study follows binomial distribution because the number of trials is finite, there are only two outcomes, (covering, and not covering mouth when sneezing ), the trial is independent
The probability distribution function for binomial distribution is
[tex]P(x=8)=n C_X\times p^x\times (1-p)^{n-x}[/tex]
Generally, the probability that among 12 randomly observed individuals exactly 8 does not cover their mouth when sneezing is mathematically represented as
[tex]P(x=8)=12c_8\times (0.267)^8\times (1-0.267)^{12-8}[/tex]
[tex]p(x=8)=495\times 0.000025828\times 0.2886794[/tex]
[tex]p(x=8)=0.0037[/tex]
Generally, the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
[tex]p(x < 5)=[p(x=0)+......+p9x=4)][/tex]
[tex]p(x < 5)=[12c_0\times(0.267)^0\times(1-0.267)^{12-0}+........+12c_4\times(0.267)^4\times (1-0.267)^{12-4}[/tex]
[tex]p(x < 5)=0.02406+0.10516+0.21067+0.25580+0.20964[/tex]
[tex]p(x < 5)=0.805[/tex]
Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as
[tex]p(x > 6)=1-p(x\leq 6)[/tex]
[tex]p(x > 6)=1-[p(x=6)+......+p(x=6)][/tex]
[tex]p(x > 6)=1-[12c_0(0.267)^0\times(1-0.267)^{12-0}+....+12c_4\times(0.267)^6\times(1-0.267)[/tex]
[tex]p(x > 6)=1-[0.02406+.....+0.0519][/tex]
[tex]p(x > 6)=0.0206[/tex]
Thus
(a )randomly observed individuals exactly do not cover their mouth when sneezing
[tex]P[x=8]=0.0037[/tex]
(b) randomly observed individuals fewer than do not cover their mouth when sneezing
[tex]P[x < 5]=0.805[/tex]
(c) fewer than half covered their mouth when sneezing
[tex]P(x > 6)=0.0206[/tex]
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Related Questions
A professional baseball player earned $1,715,000 from
playing baseball last year.
An autobiography he had written last year sold 300,000
copies at a price of $24 each. He received 10% in
royalties on the book sales.
What was his total salary last year?
$
Answers
Answer:
The right answer is actually $2,435,000.00
Step-by-step explanation:
The reason is because you take 300,000 and times that by 24 then you get 7,200,000 then you take that and times it by 0.10 then you get 720,000 then you add that to the 1,715,000 and you get 2,435,000.
300,000 x 24 = 7,200,000
7,200,000 x 0.10 = 720,000
720,000 + 1,715,000 = 2,435,000
So, $2,435,000.00 is your answer.
The total salary last year was $2,435,000 if a professional baseball player earned $1,715,000 from playing baseball last year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A professional baseball player earned $1,715,000 from playing baseball last year.
The total earning from autobiography = 300,000x24
= 7,200,000
The royalty amount = 10% of 7,200,000
The royalty amount = 0.10x7,200,000
The royalty amount = 7,200,00
Total salary last year = 1,715,000 + 7,200,00
Total salary last year = $2,435,000
Thus, the total salary last year was $2,435,000 if a professional baseball player earned $1,715,000 from playing baseball last year.
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During winter vacation, you learn that a polar jet stream is traveling across the United States. The forecaster says there will be big changes in the weather as the jet stream moves past your town in Florida.Look at the map. Predict what will happen in Florida due to the jet stream. *
A) Cooler temperature
B) Sea breeze
C) Warmer temperature
D) Land breeze
Answers
Land breeze is the answer
The points C, D, E and F all lie on the same line segment, in that order, such that the ratio of CD:DE:EFCD:DE:EF is equal to 3:2:1.3:2:1. If CF=42,CF=42, find DF.DF.
Answers
Answer:
2
Step-by-step explanation:
The required length of the DF on the line segment is 21 units.
Given that,
The points C, D, E, and F all lie on the same line segment, in that order, such that the ratio of CD:DE: EF is equal to 3:2:1, If CF=42,
To determine the length of the segment DF
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Total of the ratios
CF = 3x + 2x + 1x
CF = 6x
6x = 42
x = 7
Now,
DF = DE + DF
DF = 2x + 1x
DF = 2 * 7 + 7
DF = 14 + 7
DF = 21
Thus, the required length of the DF on the line segment is 21 units.
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Juan is saving money to buy a basketball that cost $40. He currently has $12 and will start saving $3.50 each week until he has enough money to make his purchase What is the fewest possible number of weeks that it will take for Juan to have enough money saved to buy the basketball? A) 4 B) 8 C) 12 D) 15
Answers
Answer:
b) 8
Step-by-step explanation:
eight less than four times a number is twelve. what is the number? the options are, 5 , 1 , -3 , -5 , please i need a answer asap.
Answers
What do you notice about rectangles and
parallelograms? What is the same or different between
these two polygons?
Answers
Answer:
both have four sides and equal measures with the opposite side. Parallelograms are slanted while the rectangles are straight.
A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long.If he paints 1/2 of the wall blue, how many square feet will be blue?
Answers
the area of a square patio is 196 square feet how long is each side of the patio
Answers
Answer:
[tex]14[/tex] ft
Step-by-step explanation:
Let x be the length of each side
Turn it into an algebraic expression: [tex]x^{2} = 196[/tex] 14 × 14 = 196So, x = 196I hope this helps!
Drag the expressions to the correct locations on the image. Not all expressions will be used.
Consider this quotient.
Use long division to rewrite the quotient in an equivalent form as , where is the quotient, is the remainder, and is the divisor.
Answers
Answer:
x+2 + (-5x+4)/(x^2-2x+1)
See attached
Step-by-step explanation:
Equivalent expression to represent the given division in quotient , remainder and divisor form is equals to [tex](x+2)+\frac{-5x+4}{x^{2} -2x+1}[/tex].
What is division?" Division is defined as the distribution of the given quantity into equal parts as per the conditions apply."
According to the question,
Given expression,
[tex](x^{3} -8x+6)[/tex] ÷ [tex](x^{2} -2x +1)[/tex]
As shown in long division we get,
Quotient [tex]q(x) = x+2[/tex]
Remainder [tex]r(x) = -5x+4[/tex]
Divisor [tex]b(x) = x^{2} -2x +1[/tex]
Represent quotient , remainder and divisor in an equivalent form of given expression we get,
[tex](x^{3} -8x+6)[/tex] ÷ [tex](x^{2} -2x +1)[/tex] = [tex](x+2)+\frac{-5x+4}{x^{2} -2x+1}[/tex]
Hence, equivalent expression to represent the given division in quotient , remainder and divisor form is equals to [tex](x+2)+\frac{-5x+4}{x^{2} -2x+1}[/tex].
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An average person consumes 2,000 calories each day
Answers
Gillian bakes 216 cookies on Monday. She bakes 151 more cookies on Tuesday than on Monday. She bakes 85 cookies on Wednesday. How many cookies did she bake in all? Explain.
Answers
Answer:
452
Step-by-step explanation:
216+151+85=452
Which source of bias is most relevant to the following situation:
A study is conducted with people who experienced a serious accident resulting in head trauma.
O self-interest study
O voluntary response bias
Ononresponse bias or missing data
Operceived lack of anonymity
O loaded or leading question
Answers
perceived lack of anonymity is the correct answer
The self-interest study bias will be the most relevant for the provided situation option (A) is correct.
What is bias?An attitude or prejudice either in favour of or against something or someone is referred to as a bias.
We have the situation:
A study is conducted with people who experienced a serious accident resulting in head trauma.
As we know, when researchers are invested in the outcome, bias may result.
Thus, the self-interest study bias will be the most relevant for the provided situation option (A) is correct.
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Which of the following is closest to 1/2 + 1/3
Answers
Answer:
The answer is 5/6.
Step-by-step explanation:
1/2=3/6, and 1/3=2/6. 2/6+3/6=5/6
The number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.
What is the fraction number?A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,
[tex]\dfrac{a}{b}[/tex]
Here, (a) is the numerator and (b) is the denominator.
We have to find the addition of two fraction number 1/2 and 1/3. Suppose the value which is closest to 1/2 + 1/3 is n. Thus,
[tex]n=\dfrac{1}{2}+\dfrac{1}{3}\\[/tex]
Cross multiply to find the addition of two numbers,
[tex]n=\dfrac{3+2}{6}\\n=\dfrac{5}{6}\\n=0.833[/tex]
Thus, the number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.
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Many states run lotteries to raise money. A website advertises that it knows "how to increase YOUR chances of Winning the Lottery." They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a "lucky" number to play, but maybe some numbers are luckier than others. Let's use a simulation to see how well this system works. To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number. Any value can be picked, but for this exercise, pick 1 as the lucky number. What proportion of the time do you win? Run 60 trials using the random numbers given below, starting with the first number. 89064 27308 64568 14121 98226 65388 58732 85801 69902 78431 10380 42006
Answers
Answer:
10 percent
Step-by-step explanation:
hello,
from this question, it has been stated that the lucky number is 1
from all of these values below we are to account how many times 1 appeared in these numbers have
89064, 27308, 64568 ,14121, 98226, 65388, 58732, 85801, 69902, 78431, 10380, 42006.
the total number of 1 is 6
= 6 x 1 divided by the number of trials 60
= 6 x 1/60
= 0.1
to get the proportion, we multiply 0.1 by 100
0.1 x 100
= 10%
solve the equation:
-5|3x+8|-5=-2
Answers
Answer:
x = -2 13/15
Step-by-step explanation:
-5(3x+8)-5=-2
start by multiplying out the 5 to the numbers in the parenthesis.
= -15x-40-5=-2
subtract 5 from -40
=15x-45=-2
add the 45 to itself to get rid of it and add it to -2
=15x=43
divide 43 by 15
=2.8666666666 or -2 13/15
DOU WUL IU LI TU
23. A man and a woman share a prize of $1000 between them in the
ratio 1:4. The woman shares her part between herself, her mother
and her daughter in the ratio 2:1:1. How much does her daughter receive?DOU WUL IU LI TU
23. A man and a woman share a prize of $1000 between them in the
ratio 1:4. The woman shares her part between herself, her mother
and her daughter in the ratio 2:1:1. How much does her daughter receive?
Answers
Number of parts = 1 + 4 = 5
Sum of all parts = $1000
Each part =
= 1000 ÷ 5
= $200
Money the man got =
= 200 × 1
= $200
Money the woman got =
= 200 × 4
= $800
The womans has $800 as her share .
Total parts = 2 + 1 + 1 = 4 parts
Sum of all parts = 800
Each part = 800 ÷ 4
Each part = 200
Then ,
The woman gets =
= 200 × 2
= $400
Her mother gets =
= 200 × 1
= $200
Her daughter gets =
= 200 × 1
= $200∴ Her daughter receives $200 .
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answers
I need help Please I will give lots of points
Answers
Answer:
8
Step-by-step explanation:
Answer:
105/4 = 26 2/5
Step-by-step explanation:
You charge $5.50 an hour for babysitting. At the end of the week you earn $82.50. How many hours did you work this week?
Answers
Answer:
15 hours.
Step-by-step explanation:
Which expression is rational?
4.121221222…
square root of 36
square root of 21
1.192744502…
Answers
Answer:
1 and 4
Step-by-step explanation:
because the square roots are always irrational. however, a rational number can be expressed as a decimal, fraction, and others...
Hope that helped
Answer:
the answer would be a or b
Step-by-step explanation:
because they both can be written as fraction
hope this helps you!
One method of trying to find the area of a polygon is to decompose the polygon
Is that true or false?
Answers
Answer: True
You can break the polygon up into smaller pieces such as triangles. Find the area of each triangle, and then add up those smaller areas to get the overall total area.
Answer:
i don't know
Step-by-step explanation:
learn before asking it enbarrases your self
Choose the true statement.
0-2<-3
O-2» -3
O -2 = -3
Answers
Is x=-4 a solution to the equation —3z + 10 = 5?
Answers
Answer:
No.
Step-by-step explanation:
First, note that there is no variable x inside the equation. Therefore, there is nothing for the -4 to plug into.
However, if you meant to put the same variable, it still will not work.
Plugging in -4 for z (if you meant z = -4), would give you the following:
Assuming that z = -4
-3(-4) + 10 = 5
-12 + 10 = 5
-2 ≠ 5.
Therefore, even if you did mean to put the same variable, it will still not be correct.
~
For the given equation, there is no variable x but z is a variable in the linear equation. Since x is not a variable of the equation, we can't put the value given.
But if we plug the value of -4 in place of z:
➝ -3(-4) + 10
➝ 12 + 10
➝ 22 which is not equals to 5.
Hence, this equation is not satisfying for the value of variable given that is 4. Thus, -4 is not a solution to the given equation[tex].[/tex]
Carry On Learning !
what is the next number in the patter
2, 7, 12, 17
Answers
Answer:
22
Step-by-step explanation:
Add 5
Answer:
2, 7, 12, 17, _____
the pattern is increasing by 5, so add 5 to 17
you get 22 as your answer
Step-by-step explanation:
7 1/4 × 2²+(8 1/2-2)÷3
giving brainliest
Answers
Answer:
187/6
Step-by-step explanation:
Simplify the following:
(7 + 1/4) 2^2 + (8 + 1/2 - 2)/3
2^2 = 4:
(7 + 1/4) 4 + (8 + 1/2 - 2)/3
Put 7 + 1/4 over the common denominator 4. 7 + 1/4 = (4×7)/4 + 1/4:
(4×7)/4 + 1/4 4 + (8 + 1/2 - 2)/3
4×7 = 28:
(28/4 + 1/4) 4 + (8 + 1/2 - 2)/3
28/4 + 1/4 = (28 + 1)/4:
(28 + 1)/4×4 + (8 + 1/2 - 2)/3
28 + 1 = 29:
29/4×4 + (8 + 1/2 - 2)/3
29/4×4 = (29×4)/4:
(29×4)/4 + (8 + 1/2 - 2)/3
(29×4)/4 = 4/4×29 = 29:
29 + (8 + 1/2 - 2)/3
Put 8 + 1/2 - 2 over the common denominator 2. 8 + 1/2 - 2 = (2×8)/2 + 1/2 + (2 (-2))/2:
29 + ((2×8)/2 + 1/2 + (2 (-2))/2)/3
2×8 = 16:
29 + (16/2 + 1/2 + (2 (-2))/2)/3
2 (-2) = -4:
29 + (16/2 + 1/2 + (-4)/2)/3
16/2 + 1/2 - 4/2 = (16 + 1 - 4)/2:
29 + ((16 + 1 - 4)/2)/3
16 + 1 = 17:
29 + ((17 - 4)/2)/3
| 1 | 7
- | | 4
| 1 | 3:
29 + (13/2)/3
13/2×1/3 = 13/(2×3):
29 + 13/(2×3)
2×3 = 6:
29 + 13/6
Put 29 + 13/6 over the common denominator 6. 29 + 13/6 = (6×29)/6 + 13/6:
(6×29)/6 + 13/6
6×29 = 174:
174/6 + 13/6
174/6 + 13/6 = (174 + 13)/6:
(174 + 13)/6
| 1 | 7 | 4
+ | | 1 | 3
| 1 | 8 | 7:
Answer: 187/6
Answer:
31 1/6
Step-by-step explanation:
7 1/4 × 2²+(8 1/2-2)÷3
Using PEMDAS
Parentheses first
7 1/4 × 2²+(6 1/2)÷3
Then exponents
7 1/4 × 4+(6 1/2)÷3
Changing the mixed numbers to improper fractions
7 1/4 = (4*7+1)/4 = 29/4 and ( 2*6+1)/3 = 13/2
29/4 × 4+(13/2)÷3
Multiply and divide from left to right
29 + 13/2÷3
Using copy dot flip
29 + 13/2 * 1/3
29 + 13/6
Changing back to a mixed number
13/6 = 12/6 + 1/6 = 2 1/6
29 + 2 1/6
Add
31 1/6
Select all the ratio that are equivalent to 8:6.
A. 4:3
B. 6:8
C. 16:12
D. 10:8
E. 7:5
Answers
4:3 and 16:12
4 times 2 is 8
3 times two is 6 therefore
4:3 has the same value
same with the second except it is 8 and 6 times 2
Answer: A and C
Step-by-step explanation: If you take the ratio and divide both sides by 2, you get the equivalent ratio 4:3. Then if you take the ratio and multiple both sides by 2, you will get the equivalent ratio 16:12. This means that both A and C are equivalent to the ratio 8:6.
The student council at Spendtoomuch High School is
planning a school dance. The table below shows the
budget for the dance.
School dance budget
Item
Funds raised
Expenses
Dance tickets
$300
DJ Denny
$ - 250
Decorations
$ - 100
What is the student council's expected profit?
$
Answers
explanation: if their budget is $300 and their total for the Dj and decorations is $350. they overspent money so they won’t profit. they will just be spending more than planned.
Answer:
-50
Step-by-step explanation:
I did it on khan academy
write each rate as a fraction in lowest terms 20 feet in 40 seconds
Answers
Answer:
1/2 feet per second.
Step-by-step explanation:
Please help thank you
Answers
I can't see the whole paper the sentences is cut
If the FDIC charges Bank D 6.1 cents per 100 dollars insured, how much must Bank D pay to insure $7.3 million in
deposits?
a. $4,4530,000
b. $445,300
C. $4,453
d. $445.30
Answers
Hope this help