Answer:
The value is [tex]P( X > 0.50) = 0.089264[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The population proportion is p = 0.47
Generally given that the sample size is sufficiently large , the mean of this sampling distribution is mathematically represented as
[tex]\mu_x = p = 0.47[/tex]
Generally the standard deviation of the sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{\frac{p(1- p )}{ n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ 0.47 (1-0.47 )}{ 500 } }[/tex]
=> [tex]\sigma = 0.0223[/tex]
Gnerally the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is mathematically represented as
[tex]P( X > 0.50) = P( \frac{ X - \mu }{ \sigma } > \frac{ 0.50 - 0.47 }{ 0.0223 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X > 0.50) = P( Z> 1.3453 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1.3453 is
[tex]P( Z> 1.3453 ) = 0.089264[/tex]
So
[tex]P( X > 0.50) = 0.089264[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample proportions of size n of a proportion p has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
Sample of 500 voters, hence [tex]n = 500[/tex].The proportion is of 0.47, hence [tex]p = 0.47[/tex]The mean and the standard deviation are:
[tex]\mu = p = 0.47[/tex]
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.47(0.53)}{500}} = 0.0223[/tex]
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.47}{0.0223}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a p-value of 0.9099.
1 - 0.9099 = 0.0901
0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
A similar problem is given at https://brainly.com/question/24663213
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. a. What is the average number of cars in the system
Answer:
4 customers
Step-by-step explanation:
Given that:
Mean Arrival rate (λ) = 4 cars per hour
Service rate (u) = 5 cars per hour
Using the queuing formula :
The average number of cars in the system can be obtained using the relation :
Number of customers in the system (L)
Number of customers in queue = (Lq)
L = Lq + (λ/u)
Lq = λ^2 / u(u - λ)
Hence,
Lq = 4^2 / 5(5 - 4)
Lq = 16/ 5(1)
Lq = 16/ 5
Lq = 3.2
L = 3.2 + (4/5)
L = 3.2 + 0.8
L = 4
Write the expression as a radical.
Answer:
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}[/tex]
Step-by-step explanation:
Let us consider the expression
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}[/tex]
Writing the expression as a radical
But, let us revise some rules:
[tex]\sqrt{a}=a^{\frac{1}{2}}[/tex]
[tex]\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
let us solve now
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}[/tex]
[tex]=5^{\frac{3}{2}}\left(ab\right)^{\frac{3}{2}}[/tex] ∵ [tex]\:5^{\frac{3}{2}}=5\sqrt{5}[/tex]
[tex]=\left(5ab\right)^{\frac{3}{2}}[/tex]
[tex]=\left(5ab\right)^{3\cdot \frac{1}{2}}[/tex]
[tex]=\left(\left(5ab\right)^3\right)^{\frac{1}{2}}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}[/tex]
[tex]=\sqrt{\left(5ab\right)^3}[/tex]
Thus,
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}[/tex]
What is the value of x when y=6
Answer:
When x = 12, y = 4.
Step-by-step explanation:
If
y
∝
x
we can write that
y
=
k
⋅
x
where k is a constant of proportionality.
Using the values given:
6
=
18
⋅
k
⇒
k
=
1
3
y
=
1
3
⋅
12
=
4
What is the value of x?
ans is 21
Step-by-step explanation:
you see the right angle plus 15 degree angle equal to the 5x angle
so the quation is
90+15=5x
105=5x
21=x
. 90 decimeters = _______________ millimeters
(5n - 3) - (-2n + 7)
Answer:
7n-10
Step-by-step explanation:
=(5n-3) - (-2n) -7 [Bracket Opens]
=5n - 3 +2n -7 [- × - = +]
=7n - 10 [ addition]
Find the perimeter of the following shapes to 1 d.p take r =3.14
Answer:
The perimeter is 19.7
Step-by-step explanation:
The question is not complete and there is no attachment. Nevertheless, we can make do with the given information.
we can picture that the shape is a circle and we are required to find the perimeter/circumference of the circular shape
Given
The radius r= 3.142
Step two:
the perimeter/circumference is expressed as
C=2πr
C= 2*3.142*3.142
C= 19.7
4x – 4y = -16
please help find the y value
Answer: y=x+4
Step-by-step explanation:
if you need to find the y
we divide the equation by 4
x-y=-4
add y on both sides
y=x+4
What describes θ when an ellipse is created from an intersection of a plane and double-napped cone?
θ = α
θ = 90⁰
α < θ < 90⁰
0⁰ ≤ θ < α
Answer:
C: a < θ < 90%
Step-by-step explanation:
Using the table below, evaluate whether a monkey's age in years is a function of its height in inches.
Answer:
There is no function since there is no association between all the numbers
Step-by-step explanation:
If you were to put them in a graph they would be every where and make there be no function.
HeEeEEeLpPpp <<3<3<3<3
Answer:
h = 13
Step-by-step explanation:
20 - 7 = 13
1 + 1 = ?
I am a Collage Student and i have ZERO idea what this is.
Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 15001500 hours and a mean life span of 16,00016,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 18,09918,099 hours.
Answer:
0.0809
Step-by-step explanation:
Given that :
Mean(m) = 16000
Standard deviation (s) = 1500
Probability that the life span of the monitor will be more than 18,099
P(x > 18099)
Using the Zscore formula :
Zscore =(x - m) / s
Zscore = (18099 - 16000) / 1500
Zscore = 2099 / 1500
Zscore = 1.399
P(Z > 1.399)
Using the Z probability calculator :
P(Z > 1.399) = 0.080906
= 0.0809
5) Every hour, your sister can make the same number of socks. If in the 3rd hour of work, she has
made 6 pairs of socks, and by the 5th hour, she has made 10 pairs of socks, what is the rate at which
she made the socks?
Answer: 2
Because if shes in the 3rd hour and made six pairs count up to the 5th hour and there you go you have 2!
Multiplication sentences:
3÷5=2 2+3=5
Hope this helps!
9. One winter day, the temperature increased from a low of -5 °F to a high of 40 °F. By how many degrees did the temperature change? © 25 °F A) 45 °F F B 35 °F D 55 °F
Answer:
The temperature changed by 45°F .
Step-by-step explanation:
-5°F to 0°F = 5°F and 0°F to 40°F = 40°F
5° + 40° = 45°F
what is the difference of the fractions? 5/6 - 4/6
Answer
[tex]--------------------------------------------[/tex]
[tex]\frac{5}{6}-\frac{4}{6}[/tex] = [tex]\frac{1}{6}[/tex]
[tex]0.8333333333[/tex] - [tex]0.6666666667[/tex] = [tex]0.1666666666[/tex]
[tex]\frac{1}{6}[/tex] = [tex]0.1666666666[/tex]
[tex]It's[/tex] [tex]\frac{1}{6}[/tex] [tex]because[/tex] [tex]5-4[/tex] = [tex]1[/tex]
[tex]and[/tex] [tex]the[/tex] [tex]denominator[/tex] [tex]is[/tex] [tex]the[/tex] [tex]same.[/tex]
[tex]So[/tex], [tex]it's[/tex] [tex]\frac{1}{6}[/tex]
[tex]--------------------------------------------[/tex]
Hope this helps! <3
[tex]--------------------------------------------[/tex]
2./10
To rationalize the denominator of
311
you should multiply the expression by which fraction?
Complete Question:
To rationalize the denominator of 2√10/3√11 , you should multiply the expression by which fraction?
Answer:
Multiply by [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2\sqrt{10}}{3\sqrt{11}}[/tex]
Required
To rationalize
To do this, we simply multiply the expression by the fraction of [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]
This gives:
[tex]\frac{2\sqrt{10}}{3\sqrt{11}} * \frac{\sqrt{11}}{\sqrt{11}}[/tex]
[tex]\frac{2\sqrt{10 * 11}}{3\sqrt{11 * 11}}[/tex]
[tex]\frac{2\sqrt{110}}{3\sqrt{121}}[/tex]
Express [tex]\sqrt{121[/tex] as 11
[tex]\frac{2\sqrt{110}}{3*11}[/tex]
[tex]\frac{2\sqrt{110}}{33}[/tex]
Hence:
[tex]\frac{2\sqrt{10}}{3\sqrt{11}}[/tex] = [tex]\frac{2\sqrt{110}}{33}[/tex]
4x + 2x + 2 = 3x - 7
How many solutions
Answer:
One solution (x = -3)
Step-by-step explanation:
4x + 2x + 2 = 3x - 7
6x + 2 = 3x - 7
3x = -9
x = -3
find the multiplicative inverse of 7 in mod 9
Answer:
-1/7
Step-by-step explanation:
The inverse of 7 is simply the opposite
Victoria is an actuary for an insurance company. She recently compiled this table to help her determine health insurance premiums for the upcoming year. Consider the likeliness of each individual to have a need for health insurance. Order the individuals from least to greatest need for health insurance. Profile Description Probability of Visiting a Doctor for Injury or Illness This Year 18-year-old male athlete 16% 78-year-old male nonsmoker 53% 65-year-old female smoker 76% 26-year-old female nonsmoker 14% 45-year-old male smoker 39% 32-year-old female nonsmoker 20%
Answer:
Here is the order (considered % at the end to be a criteria)
26-year-old female nonsmoker 14% 18-year-old male athlete 16% 32-year-old female nonsmoker 20%45-year-old male smoker 39% 78-year-old male nonsmoker 53% 65-year-old female smoker 76%Answer:
26
18
32
45
78
65
least to greatest
What is 1/2 divided by 1/4 in the simplest form?
Answer:
2
Step-by-step explanation:
1/2 divided by 1/4 rewritten is 1/2 times 4/1 equels 4/2. In its simplest form 2.
1/2 divided by 1/4 in the simplest form is 2.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Given that the expression 1/2 divided by 1/4.
simplifying,
1/2 divided by 1/4 = 1/2 ÷ 1/4
Rearranging into the multiplication form,
1/2 divided by 1/4 = 4/2
1/2 divided by 1/4 = 2
Therefore, the simplest form of 1/2 divided by 1/4 is 2.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ2
What is the Y and X in this problem?
Answer:
there is no problem
Step-by-step explanation:
Which equation can be used in system of equations to solve for the unknown? CHECK ALL THAT APPLY
1) A=2
2) -6A+B=2
3) 3A-B+C=1
4) B=0
5) 9A-3B+C=1
Answer:
A and E
Step-by-step explanation:
edge 2021
Answer:
Option A and E are the correct answers.
Evaluate the expression 9 + (7 - 4)2 + 3.
06
O3
0 18
O 12
Answer:
18
Step-by-step explanation:
PEMDAS
Parenthesis
Exponents
Multiply/Divide (from left to right)
Add/Subtract (from left to right)
Ali took five Math tests during the semester and the mean of his test score was 85. If his mean after the first three was 83, What was the mean of his 4th and 5th tests
Answer:
88
Step-by-step explanation:
Mean of five test = 85
Sum of five tests = 85*5 = 425
Mean of first three test =83
Sum of first three test = 83 * 3 = 249
Sum of 4th and 5th test scores = 425 - 249
= 176
Mean of his 4th and 5th test = 176/2 = 88
in hostel of 40 students there is food for 30 days if 20 more students join the hostel how long will the food last
Answer:
The food will last for 20 days
Step-by-step explanation:
The equation of the inverse proportional is xy = k, where k is the constant of variation
∵ In a hostel of 40 students, there is food for 30 days
→ That means the food is the constant k and the number of days y
varies inversely with the number of students x
∴ x = 40 and y = 30
∵ xy = k
∴ 40 × 30 = k
∴ 1200 = k
∴ The equation of the inverse proportional is xy = 1200
∵ 20 more students join the hostel
→ That means the number of students increased by 20
∴ The number of students in the hostel = 40 + 20
∴ The number of students in the hostel = 60
→ By using the equation above
∵ 60 × y = 1200
∴ 60y = 1200
→ Divide both sides by 60
∴ y = 20
∴ The food will last for 20 days
There are 1/2 as many eighth graders in the choir as seventh graders. There are 48 eight graders. Write and solve an equation to find the number of seventh graders in the choir. (This problem needs to be written as an equation..not just 48x2) Thanks
Answer:
Step-by-step explanation:
Let x represent the number of seventh graders in the choir:
48=x/2
x=96
What type of triangle is this?
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible
Answer:
HL
Step-by-step explanation:
In both triangle, hypotenuse and one leg is congruent. So, HL congruent
Which recursive definition produces an arithmetic sequence where g(5) = 8 and g(10) = 10?
Answer:
gₙ = gₙ₋₁ + 0.4, with g₁ = 6.4
Step-by-step explanation:
The n-th term of an arithmetic sequence can be written as:
gₙ = g₁ + (n - 1)*d
Where g₁ is the first value, and d is the difference between any two consecutive terms of this sequence.
Then we have the equations:
g₅ = 8 = g₁ + (5 -1)*d
g₁₀ = 10 = g₁ + (10 - 1)*d
This is a system of equations, we can rewrite this as:
8 = g₁ + 4*d
10 = g₁ + 9*d
To solve this, the first step will be isolate one of the variables in one of the equations, i will isolate g₁ in the first equation:
g₁ = 8 - 4*d
Now we can replace this in the second equation to get:
10 = 8 - 4*d + 9*d
10 = 8 + 5*d
10 - 8 = 5*d
2 = 5*d
2/5 = d = 0.4
Now with this, we can find the value of g₁ by using the equation:
g1 = 8 - 4*d = 8 - 4*(2/5) = 8 - 8/5 = 6.4
Then the nth term of this sequence can be written as:
gₙ = 6.4 + (n - 1)*0.4
This relation also can be written as:
gₙ = gₙ₋₁ + d = gₙ₋₁ + 0.4, with g₁ = 6.4
Then the correct option is the second option.
PLEASE HELP I WILL MARK BRAINLIST TO WHOEVER ANSWERS FIRST !!
graph the line that represents the equation y=2/3x+1
I HAVE THE PICTURE OF THE GRAPH ABOVE !!
Answer:
Graph (6, 5) and (-6, -3), and then use a ruler (optional), and draw a line between them, and a little after the points.
Step-by-step explanation:
y = 2/3x + 1
Substitute different numbers for x, and find y:
You don't really want to work with fractions, so try to find a number that when multiplied by 2/3, gives you a whole number
x = 6
y = 2/3(6) + 1
y = 12/3 + 1
y = 4 + 1
y = 5
Point: (6, 5)
x = -6
y = 2/3(-6) + 1
y = -12/3 + 1
y = -4 + 1
y = -3
Point: (-6, -3)
Graph these two points, and then use a ruler (optional), and draw a line between them, and a little after the points.