Answer:
a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the question.
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.
63% of US adults opposed to taxes on junk food and soda.
This means that [tex]p = 0.63[/tex]
You randomly select 10 US adults.
This means that [tex]n = 10[/tex]
(a) exactly one
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
(b) at least four
This is
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
[tex]P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063[/tex]
[tex]P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285[/tex]
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644[/tex]
0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
(c) less than eight
This is
[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]
In which
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529[/tex]
[tex]P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578[/tex]
[tex]P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205[/tex]
[tex]P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795[/tex]
0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
A university considers giving only pass/fail grades to freshmen to reduce competition and stress. The student newspaper interviews faculty members and reports their opinions of the proposed policy. Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed. The goal is to find the probability that a majority (26 or more) will favor the proposal.
Answer:
0.9983 = 99.83% probability that a majority will favor the proposal.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed.
This means, respectively, that [tex]p = 0.7, n = 50[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 50*0.7 = 35[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.7*0.3} = 3.24[/tex]
Probability that a majority (26 or more) will favor the proposal.
Using continuity correction, this is [tex]P(X \geq 26 - 0.5) = P(X \geq 25.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 25.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25.5 - 35}{3.24}[/tex]
[tex]Z = -2.93[/tex]
[tex]Z = -2.93[/tex] has a pvalue of 0.0017
1 - 0.0017 = 0.9983
0.9983 = 99.83% probability that a majority will favor the proposal.
A number, x, rounded to 1 decimal place is 3.7
Write down the error interval for x.
Answer: (3.65, 3.74)
Step-by-step explanation:
Now, when we round a number to a given decimal place, we need to look at the decimal to the left of the decimal place where we are rounding.
if it is 5 or more, we round up
if it is smaller than 5, we round down.
Then for example, if we want to round:
4.534
to the first decimal place, we need to look at the second decimal place.
we can see that it is a 2.
Then we round down, and get:
4.5
Now we know that, when rounding to the first decimal place, we have:
x = 3.7
Then the maximum value that x could have is:
x = 3.74 (because here we round down to 3.7)
and the minimum value that x could have is:
x = 3.65 (because here we round up to 3.7)
Then the error interval for x is:
(3.65, 3.74)
Triangle A is transformed by the
combined transformation of a rotation
of 180° about the point (-1,0) followed
by a translation with vector
-3
2)
One point on triangle A is invariant
under the combined transformation.
What are the coordinates of this point?
Answer:
( -2.5 , 1 )
Step-by-step explanation:
(-2.5 ,1 ) hope this helps u
In which expression should the exponents be multiplied
Answer:
when the bases are different and the powers are same
Step-by-step explanation:
(a)²★(a)³=(a)²+³........
A group of high school students are volunteering for Habitat for Humanity during their summer break. They
are putting the finishing touches on a house they built. Working alone, Kendra can paint a certain room in 7
hours. Joe can paint the same room in 6 hours. Write an equation that can be used to find how long it will
take them working together to paint the room. How many hours will it take them to paint the room? If
necessary, round your answer to the nearest tenth.
In response to the question, we may say that It will take Kendra and Joe expression approximately 3.2 hours to paint the room together.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
Let's denote the time it takes Kendra to paint the room as "K" and the time it takes Joe to paint the room as "J". We can use the formula:
[tex]1/K + 1/J = 1/T\\1/7 + 1/6 = 1/T\\13/42 = 1/T\\13T = 42\\[/tex]
Therefore, T = 42/13 ≈ 3.2 hours (rounded to the nearest tenth).
It will take Kendra and Joe approximately 3.2 hours to paint the room together.
To know more about expression visit :-
https://brainly.com/question/14083225
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Allison earns a 10% commission on her weekly sales. Each week, she puts of her commission in a savings account and uses the amount remaining on bills. If Allison's sales for one week were $2,300.00. how much money does she use for bills?
Answer:
$2,070 is how much she will use for bills.
Evaluate the expression (14 − 4)2 ÷ 10.
The value of the expression is value of
Answer:
2
Step-by-step explanation:
PEMDAS says to do the equations in parentheses first
(14-4) = 10
PEMDAS then says to do multiplication or division, whichever comes first in the equation, which is multiplication in this case
(10)2 = 20
20 ÷ 10 = 2
I will give you Brianlyist
Answer:
what do you need help with?
Step-by-step explanation:
**you will get a real answer i promise**:)
Answer:
I don't understand the problem
Pl help it’s for a grade
A.
Hope this helps. :))))
If each person gets a 1/2 gallon of water, then how many people can share 64 gallons of water?
Answer: 128 people
Step-by-step explanation:
every 2 people get a gallon so 2*64=128
simplify the first expression 5(m+1)-1=
Answer:
-0.8/ -4/5
Step-by-step explanation:
5(m+1) -1 = 0
5m +5 -1 = 0
5m +4 =0
5m= -4
m= -4/5
Which of the following is true of a radius of a circle?
(1) Radius is twice the diameter in any circle
(2) Radius is the distance from the center to any point on the circle.
(3) All radii in circles have the same value.
The second one is correct (Radius is the distance from the center to any point on the circle)
Answer:
2.)
Step-by-step explanation:
The radius of any circle is the distance from the EXACT center, to any point of the circle.
The wages
w
(in £) Gordon earns is the number of hours he works
n
multiplied by his hourly rate
r
(in £ per hour). Enter a formula for Gordon's wages and enter the wage he would earn if he worked 5 hours at a rate of £10.40 per hour
n×r=£w
That is the equation you would use. Just put 5 in place of the N, and £10.40 in place of the R
Solve each of the systems below by substitution
y = -3/2x (fraction)
3x + 2y = -4
Answer:
GET PHOTOMATH
Step-by-step explanation:
DOWNLOAD PHOTOMATHhope this helps bro :)kate pays $203 in advance on her account at the athletic club. Each time she uses the club, $9 is deducted from the account. Find the remaining in the account after 12 visits
Answer:
95
Step-by-step explanation:
The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.
-y^2 =25y+6y^3
find y
Answer:
y=0
Step-by-step explanation:
Hope this helps you.
What is the measure of the missing angle?
Answer:
115
Step-by-step explanation:
To find the missing angle all you have to do is add the 2 nonadjacent interior angles which are 75 and 40 to get the exterior angle which is 115.
Hope this helps!:)
a woman spent 3/5 of her weekly salary on rent and 25% of her weekly salary on food. Her food cost $2500. How much did she spend on rent
Answer:
$6,000
Step-by-step explanation:
If her food costed $2500 and was 25%, then she had $10,000 to begin with. 3/5 of $10,000 is $6,000, so her rent costs $6,000.
Answer:
$6,000 on rent
Step-by-step explanation:
Find her weekly salary by dividing 2500 by 0.25
2500/0.25
= 10,000
Now, find how much she spent on rent by multiplying 10,000 by 3/5
10,000(3/5)
= 6,000
So, she spent $6,000 on rent
Can someone help me please ?
Step-by-step explanation:
For A
The name of two similar triangles is ABC and CED.
For b
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
Here
< BAC = < CED ( given)
<ACB = < ECD ( vertically opposite angles)
No need to answer :)
Answer:
okay, we'll leave you to it
good luck
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Calculate the area of the trapezoid, which is not drawn to scale.
Answer:
38 in
Step-by-step explanation:
Ok, so the bottom part is a rectangle and the top part is a triangle. We’re gonna split those into two different shapes.
8 * 4 = 32, this is the area of the bottom rectangle.
To get the side length of the top triangle, we have to subtract 8 from 11.
11 - 8 = 3
(3 * 4)/2 = 6, this is the area of the top triangle.
Add the two areas, 32 + 6 = 38
And that’s it, maybe, I think.
3
Choose all the expressions that are equal to
A.
8
15
5
11
B.
7
12
+
6
C. 5
6
-
1
12
D.
5. 1+
E.
7
20
3
5
Answer:
the answers (D)
Step-by-step explanation:
6. Y(3.5, 1), Z(-4, 2.5)
Please help
Answer:
Answer given below
Step-by-step explanation:
5. Root 104 = 10.1
10.1 x 0.5 = 5.05 miles
What’s this shape called?
Answer:
This shape is called triangle
A number x decreased by 6 is at most 11.
Answer:
17?
Step-by-step explanation:
Store A sells 12 juice bottles for $4 and store B sells 18 juice bottles for $6. Are these rates equivalent? Explain your reasoning.
Answer:
these rates are equivalent.
12bottles/$4= 18bottles/$6= 3bottles/$1
Step-by-step explanation:
A new car loan has monthly payments of $482.75. How much money will be paid on the car loan after 3 years?
========================================================
Work Shown:
1 year = 12 months
3*(1 year) = 3*(12 months) ..... multiply both sides by 3
3 years = 36 months
You'll make 36 payments, each being $482.75, which means the total amount of money paid is 36*482.75 = 17,379 dollars
Can somebody solve this for me please?
Answer:
D
Step-by-step explanation:
[tex] {3}^{x ^{2 - 1} } = \frac{ {27}^{ - x} }{3 } [/tex]
Answer:
-1/4
Step-by-step explanation:
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
Answer:
where are the choices?
Step-by-step explanation:
Where are the choices?