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.
What is the value of the expression below? |6| + |-4|
Answer:
Your answer is 10
Step-by-step explanation:
The absolute value of |6| = 6
The absolute value of |-4| = 4
6 + 4 = 10, your answer!
Hope this helped :)
Answer:
10
Step-by-step explanation:
1. I6I + I-4I
Everything inside the absolute value comes out positive. So
2. 6+4
Add numbers together
3. 10
What is the product?
(X^4)(3x-2)(4x2 +5x)?
Answer:
12x^7+7x^6-10x^5
Step-by-step explanation:
(X^4)(12x³+15x²-8x²-10x)
(X^4)(12x³+7x²-10x)
12x^7+7x^6-10x^5
Identify the range of the function shown in the graph.
Answer:
Identify the range of the function shown in the graph.
Answer:
range=(10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10)
Janel has $250 in her bank account and is earning $75 a week babysitting the annoying neighbor kids. April has $720 in her bank account and spends $35 a week on clothes and shoes. how long will it take for the two to have the same amount of money in their bank accounts? solve using systems of equations.
Answer:
Step-by-step explanation:
J = 250 + 75t
A = 720 - 35t
250 + 75t = 720 - 35t
110t = 470
t = 47/11 weeks = 4.3 weeks
Briana used two congruent parallelograms and a square to create the figure shown. What is the areaa of the figure Briana created in square feet?
A. 27ft²
B.24 3/4 ft²
C.67 1/2 ft²
D.33 3/4 ft²
Answer: the answer is D
Step-by-step explanation: I got it right
Find the derivative of y=(3x+5)^7 using the chain rule. Give your answer fully factored.
25/35 and 10/14 simplified
Answer:
(25/5)/(35/5)
=> 5/7
(10/2)/(14/2)
=> 5/7
Hence both of the numbers simplify to 5/7
Hope it helps
What is the decay factor that corresponds to a 99% decrease?
Answer:
It's D. 0.01
Step-by-step explanation:
Took the test
g The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people. Assume that this trend is linear and the population has been growing like this since 2000. a. Write a function for the population, P, in terms of the number of years since 2000, ????. (6 points) b. What is the slope of the function and what does it represent in the context of the problem. Include units. (5 points) c. What is the vertical intercept of the function and what does it represent? Include units (5 points) d. What do you believe the population was in 2015?
Answer:
a) [tex]P(t) = 11500 + 425t[/tex]
b) The slope is of 425 people, which is by how much the population increases each year.
c) The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d) 17,875 people.
Step-by-step explanation:
A linear function that measures population after t years has the following format:
[tex]P(t) = P(0) + at[/tex]
In which P(0) is the vertical intercept, which represents the initial population, and a is the slope, which represents the yearly population.
a. Write a function for the population, P, in terms of the number of years since 2000.
The first step is finding the slope.
Finding the slope:
The slope is the change in the output divided by the change in the input, during a period of time.
The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people.
This means that in 2009 - 2005 = 4 years, the population increased by 15325 - 13625 = 1700.
So the slope is
[tex]a = \frac{1700}{4} = 425[/tex]
So
[tex]P(t) = P(0) + 425t[/tex]
Finding the initial population:
We want to find P(0), which is the population in 2000. The population of Little Townville in 2005 was 13,625 people, which means that [tex]P(5) = 13625[/tex]. So
[tex]P(t) = P(0) + 425t[/tex]
[tex]13625 = P(0) + 425*5[/tex]
[tex]P(0) = 13625 - 425*5[/tex]
[tex]P(0) = 11500[/tex]
So
[tex]P(t) = 11500 + 425t[/tex]
b. What is the slope of the function and what does it represent in the context of the problem. Include units.
The slope is of 425 people, which is by how much the population increases each year.
c. What is the vertical intercept of the function and what does it represent? Include units
The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d. What do you believe the population was in 2015?
2015 is 2015 - 2000 = 15 years after 2000, so this is P(15).
[tex]P(15) = 11500 + 425*15 = 17875[/tex]
17,875 people.
b) Solve (2 - x)2 <25
If you need to use fractions, they can be written in the form a/b
Answer:
are you solving for x? and if you are solving for x it is x> -21/2
Step-by-step explanation:
Pythagorean theorem
please help
Answer:
c = square of a2+b2
i think its correct ome
question is down below thanks
Answer:
E
Step-by-step explanation:
A linear equation is in the form of: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
m is the slope and it's given, which is -6
b is the y-intercept and it's given, which is 9
When we plug in to the form we get:
[tex]y=-6x+9[/tex]
PLEASE HELP ASAP!!!!
Tyra made 8 fewer jackets than zack they made 48 jackets altogether how many jackets did zac make
Answer:
Zac Made 28 Jacket
okay have a nice day.
Translate the given phrase into an algebraic expression and simplify if possible: the sum of -4 and the difference of 3 and 1
Algebraic expression for the given phrase is
[tex]-4+(3-1)[/tex]
Simplified answer is -2
Given :
The given phrase is the sum of -4 and the difference of 3 and 1
To find the difference we subtract the numbers
difference of 3 and 1 is 3-1
for the sum we add it
the sum of -4 and the difference of 3 and 1
the sum of -4 and (3-1)
Now we add it , [tex]-4+(3-1)[/tex]
Algebraic expression for the given phrase is
[tex]-4+(3-1)[/tex]
Now we simplify it
[tex]-4+(3-1)\\-4+(2)\\-2[/tex]
Learn more : brainly.com/question/24513204
If 30 pounds of rice and 30 pounds of potatoes cost $33.60 and 20 pounds of rice and 12 pounds of potatoes costs $19.04, how much will 10 pounds of rice and 50 pounds of potatoes cost?
Answer:
Step-by-step explanation:
here you go
Is the graph increasing, decreasing, or constant?
O A. Constant
O B. Increasing
C. Decreasing
Answer:
increasing according to me
Step-by-step explanation:
..
Help quick pls on 5 and 6!!!pls and ty!
Answer:
I can't see the picture
nope
WILL MARK BRAINLIEST
The Miller family and the Adams family both purchased houses on the same day several years ago
The Miller family bought their house for S159,352 and it has been increasing in value by 3.7% each year.
The value of the Adams family's home since it was purchased, A(z) can be modeled by the function A(z) = 142, 809(1.04)", where a represents the number of years since the house was purchased
PartA) Which family paid more for their house?
Part B) Which family's home value is increasing at a faster rate?
Answer:
Part A: Which family paid more for their house? And at what cost.
The Miller family
Part B: Which family’s home value is increasing at a faster rate?
The Adams family
Step-by-step explanation:
What is the slope of the line that passes through the points (-4, 8) and (-14, 8) ? Write your answer in simplest form.
Answer:
the slope is 0
Step-by-step explanation:
Answer:slope, m=0
Step-by-step explanation:
using the slope formula m=y2-y1/x2-x1
m=8-8/-14-4 = 0/-10
m=0
The number of hospitals in a certain country has been declining for many years. In 2014, there were 5,727 hospitals, but, in 2017, there were only 5,571. Assuming this trend is linear, write an equation for the number of hospitals H in the this country t years since 2000.
H=
Answer:
H = -52t + 6455
Step-by-step explanation:
2014 is 14 years since 2000. That gives you the point (14, 5727).
2017 is 17 years since 2000. That gives you the point (17, 5571).
Since we have two points in the line, we can find the equation of the line.
y = mx + b
m = slope = (difference in y)/(difference in x)
m = (5571 - 5727)/(17 - 14) = -156/3 = -52
y = -52x + b
Now we use one of the points for x and y, and we solve for b.
5727 = -52(14) + b
b = 6455
The equation is
y = -52x + 6455
Using H and t, we have
H = -52t + 6455
The relationship between the number of hospitals and the years, is a linear function.
The equation for the number of hospitals is: [tex]H = -52t + 6455[/tex]
Let
[tex]t \to[/tex] years since 2000
[tex]H \to[/tex] number of hospitals since 2000
So, we have:
[tex](t_1,H_1) = (14,5727)[/tex] ---- 2014
[tex](t_2,H_2) = (17,5571)[/tex]
Calculate the slope (m)
[tex]m = \frac{H_2 - H_1}{t_2 - t_1}[/tex]
This gives:
[tex]m = \frac{5571 - 5727}{17-14}[/tex]
[tex]m = \frac{-156}{3}[/tex]
[tex]m = -52[/tex]
The linear equation is then calculated using:
[tex]H = m(t - t_1) + H_1[/tex]
So, we have:
[tex]H = -52(t - 14) + 5727[/tex]
[tex]H = -52t + 728 + 5727[/tex]
[tex]H = -52t + 6455[/tex]
Hence, the equation H is: [tex]H = -52t + 6455[/tex]
Read more about linear equations at:
https://brainly.com/question/11897796
Question 16
If n = 6, what is the value of 9n – 4?
Α.
11
B.
50
С
52
D
54
Answer is Option B) 50
9(6)-4
54-4
50
8m/3 if m = 12
Evaluate
A dog is tied with a rope to a stake in the ground. The length of the rope is 10 yards.
What is the area, in square yards, in which the dog can roam?
1) 1001
2) 100x yd.2
3) 100 yd.2
4) 20ryd.
Answer:
the area in square yards is 100πyd^2
Step-by-step explanation:
The computation of the area is shown below:
Area = πr^2
= π10^2
= 100πyd^2
Hence, the area in square yards is 100πyd^2
We simply applied the above formula to determine the area
Which describes how to calculate the range of this data set?
4,5, 6, 8, 11, 12
O Subtract 11-5.
O Subtract 12-4.
O Add 11+5.
Add 12+ 4.
Answer:
B) Subtract 12-4 to calculate the range of this data set
Theodore hired a roofer for some work. on final bill he was charged a total of 642$ .425$ was listed for parts and rest for labor . if the hourly rate was 31$ how many hours of labor was needed ?
Answer:
7 hours
So you so 642-425= 217, then you do 217/31= 7
your answer is 7
WIll GIVE BRAINLYEST TO WHOEVER ANSWERS BOTH QUESTIONS FIRST CORRECTLY
Answer:
1. 8.4 in 2. 33.6
Step-by-step explanation:
A water pipe has a circular cross section of radius 0.75 cm. Water flows through the pipe at a rate of 16 cm/s.
Calculate the time taken for 1 litre of water to flow through the pipe.
Step-by-step explanation:
volume of water flows through the pipe per second= π r² h = 22/7 × ( 3/4)² × 16
= 22/7 × 9/16 × 16
= 22/7 × 9
= 3.14 × 9 = 28.26 cm ³= 28.26/ 1000= 0.02826 litre
0.02826litre = 1 second
1 litre = 1 / 0.02826 = 100000/2826
= 35 .38 seconds
answer = 35.38 seconds
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you ☺️.
please help geometry
Answer:
(1,2)
Step-by-step explanation:
1) Ellen Murphy manages an Auto Film outlet that
applies window films to automobile windows.
She reported that last week a total of 28 autos had
window film applied. Auto Film charges $129.99
for a four-door sedan and $99.99 for a two-door
coupe. If Ellen had total receipts for the week of
$3,459.72, how many four-doors sedans had been
serviced? How many two-door coupes?
Answer:
Four-door sedan = 22
Two-door coupes = 6
Step-by-step explanation:
This is an algebra problem.
Let "x" represent number of four-door sedan,
"y" represent two-door coupe.
Since there are total of 28 autos on which film is applied, we have:
x + y = 28 Equation 1
y = 28 - x Equation 2
Also provided,
Total revenue = $3,459.72
That means,
129.99x + 99.99y = 3,459.72 Equation 3
Putting value of "y" from Equation 2 in Equation 3 we have:
129.99x + 99.99(28 - x) = 3,459.72
129.99x + 2,799.72 - 99.99x = 3,459.72
30x = 660
x = [tex]\frac{660}{30} = 22[/tex]
Therefore, number of four door sedans = 22
Further y that is two door sedan = 28 - x = 28 - 22 = 6