Answer:
3:1
Step-by-step explanation:
&%6#46+4636$7$-&&%$44
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 decay factor that corresponds to a 99% decrease?
Answer:
It's D. 0.01
Step-by-step explanation:
Took the test
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:
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 ☺️.
HELP ME FASTTTT PLSSS
what’s the reciprocal of 11/4?
Answer:
0.02272727272
You can search for any mathematical expression, using functions such as: sin, cos, sqrt, etc. You can find a complete list of functions here.
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Answer:
4/11 is the answer plz mark as brainlliest
Pl help it’s for a grade
Answer:
Constant speed
Step-by-step explanation:
That's the answer
Answer:
C.
Step-by-step explanation:
Help quick pls on 5 and 6!!!pls and ty!
Answer:
I can't see the picture
nope
The trip from Manhattan to Montauk Point is 120 miles by train or by car. A train makes the trip in 2 hours, while a car makes the trip in 2.5 hours. How much faster in miles per hour, is the average speed of the train than the average speed of the car?
Answer:
30mph faster
Step-by-step explanation:
first you must find how fast the train can go in 1 hour
that is 60mph, then multiply 60 and 2.5
60x2.5 = 150mph then,
150 - 120 =30mph
very sorry if this is wrong
The average speed of the train is 1.25 times the average speed of the car.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
The excursion from Manhattan to Montauk Point is 120 miles via train or via vehicle. A train makes the outing in 2 hours, while a vehicle makes the excursion in 2.5 hours.
The average speed of the train is given as,
⇒ 120 / 2
⇒ 60 miles per hour
The average speed of the car is given as,
⇒ 120 / 2.5
⇒ 48 miles per hour
The ratio of the average speed of the train to the car will be given as,
⇒ 60/48
⇒ 1.25
The average speed of the train is 1.25 times the average speed of the car.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ5
It takes Naomi 4 minutes to run 5 laps. How long does it take her to run 30 laps? Use a table, double number line, tape diagram or another strategy to show your thinking.
(PLEASE ANSWER ITS DUE IN 20 MINUTES!)
Answer: 24 ???
Step-by-step explanation:
4 mins to run 5 ... so im guessing it goes by 5
5 = 4
10 = 8
15 = 12
20 = 16
25 = 20
30 = 24
I am not sure if its right but that what i think ( you can use a table btw one colom that says laps and starts with 5 then the other colom that says mins and starts with 4
Hope its right Good Luck have a good rest of your day
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
A random sample of adult men was asked if they would return the money if they found a wallet on the street. Of 143 men, 29 said they would. The true proportion of all adult men who would return the money is 18%. Which of the following do you expect would accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet?
Select one or more:
a. The mean of the sampling distribution will be equal to 0.18.
b. The mean of the sampling distribution will be equal to 0.2028.
c. The sampling distribution would be approximately standard normal.
d. The sampling distribution will be skewed right.
e. The sampling distribution will be skewed left.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Answer:
b. The mean of the sampling distribution will be equal to 0.2028.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Step-by-step explanation:
We use the Central Limit Theorem to solve this question.
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].
The sample proportion being approximately normal means that option f. is correct.
Of 143 men, 29 said they would.
This means that [tex]p = \frac{29}{143} = 0.2028[/tex]
This means that option b is correct.
g. The standard deviation of the sampling distribution will be 0.0336.
Lets find the standard deviation.
Sample of 143, so [tex]n = 143[/tex]
[tex]s = \sqrt{\frac{0.2028*0.7972}{143}} = 0.0336[/tex]
So option g. is correct.
The statements that accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet are;
B) The mean of the sampling distribution will be equal to 0.2028.
F) The sampling distribution will be approximately normal.
G) The standard deviation of the sampling distribution will be 0.0336.
Central Limit Theorem.
We are given the true proportion of all adult men who will return the money as; p = 18% = 0.18
Thus, the population mean = 0.18
Now, out of 143 men, 29 said they will return the money. Thus;
Sample mean = Sample proportion = 29/143 = 0.2028
The formula for the sampling standard deviation is;
s = √[p^(1 - p^)/n]
s = √[0.2028(1 - 0.2028)/143]
s = √0.001130574545
s = 0.0336
Looking at the options and comparing to the answers gotten above, only option B, F and G are correct.
Read more about Central Limit Theorem at; https://brainly.com/question/25800303
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)
Which of the following is the slope of the line below?
O slope: m=1
O slope: m = 0
O slope: m = undefined
slope: m=3
Solve the system using substitution. Show your work and give your answers as an ordered pair.
How many kittens weigh at least - of a pound?
find the value of x
Answer:
x = 7
Step-by-step explanation:
A right angle is equal to 90 degrees
The sum of the angles, 55 and 5x, should equal 90
55 + 5x = 90
Isolate the variable
Subtract both sides by 55
55 - 55 + 5x = 90 - 55
5x = 35
Divide both sides by 5
5x ÷ 5 = 35 ÷ 5
x = 7
The lightest puppy in a litter weighs 12 ounces, which is
4/7
of the weight of the heaviest puppy.
The equation
4/7
w = 12 can be used to find the weight w in ounces of the heaviest puppy.
How much does the heaviest puppy weigh?
Answer:
46 pounds
Step-by-step explanation:
Answer:
21 pounds
Step-by-step explanation:
The sum of two numbers is 10. Their difference is 2. What are the numbers?
Answer:
6 and 4
Step-by-step explanation:
6+4 = 10
6-2 = 4
Find the derivative of y=(3x+5)^7 using the chain rule. Give your answer fully factored.
28. Write an
algebraic expression for the perimeter of the
swimming pool.
28) y + 2y + 1 + y + 2y + 1
29) y^2 + 4y + 2
30) The two expressions are equal because its the same question written in two different forms, one of the expression is written in an unsmplified form and the other expression is the simplified form.
= y + y = y^2
= 2y + 2y = 4y
= 1 + 1 = 2
= y^2 + 4y + 2
I haven't done this in a long time so I'm sorry if it's wrong
PLS HELP ME!
A ladder 25ft long leans against a vertical wall with it's foot on level ground 7ft from the base of the wall. If the foot is pulled away from the wall at the rate 2ft/s , Express the distance (yft)of the top of the ladder above the ground as a function the time t second in moving
Answer:
what is this language
Step-by-step explanation:
Answer:
hope it will help you.....
9/12 ÷ 3/12 = ??????
Answer: 9/12 ÷ 3/12 is 3.
Step-by-step explanation: Do the KFC.
K. Keep.
F. Flip the second term to 12/3.
C. Change the ÷ into ×. Then, solve.
9 x 12 is 108, and 3 x 12 is 36.
108 ÷ 36 = 3.
Pythagorean theorem
please help
Answer:
c = square of a2+b2
i think its correct ome
si un avión buela a 1200 pies de altura ¿a cuantos metros de altura se encuentra?
(1 pie=30.5 CM)
Answer:
30.5x1200=36600
r=el avion vuela a 36.600m de altura
What is the sum of -3/7
Answer:
-0.4285714286
Step-by-step explanation:
-3/7 = -0.4285714286
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
John has 6 pairs of pants and 3 shirts. How many possible outfits consisting of one shirt and
one pair of pants can he select?
Answer:
4*5*7=140 ways
Step-by-step explanation:
First he has to decide on a pair of pants and he has 4 different choices.
For each of those choices he has a choice of 7 different shirts, so that gives him 4 times 7 = 28 different pant/shirt combinations. (I hope none of the pants are striped and none of the shirts have polka-dots).
For each those 28 possibilities, he has 5 different ties he could select, so altogether he has 28 times 5 = 140 different outfits, and some of them may be acceptable to wear in public.
It is simply , 4*5*7=140 ways.
Explain how to isolate the variable in this equation -2/5x+7=15
Answer:
[tex]x = -20[/tex]
Step-by-step explanation:
Use inverse operations and simplification to isolate the variable in the equation.
[tex]-\frac{2}{5}x + 7 = 15\\-7\\\\-\frac{2}{5}x = 8\\[/tex]
Now divide the equation by [tex](-\frac{2}{5})[/tex] remember, dividing a fraction is the same as multiplying by the reciprocal. The reciprocal of a fraction is when one switches the places of the numerator (number on top of a fraction bar), and the denominator (number on the bottom of the fraction bar).
[tex]-\frac{2}{5}x = 8\\[/tex]
÷[tex]-\frac{2}{5}[/tex]
[tex]x = 8 * (-\frac{5}{2})[/tex]
Simplify,
[tex]x = 4 *(- 5)\\\\ x= -20[/tex]
please help me
[tex]4 \sqrt{144a {12b {3}^{?} }^{?} } [/tex]
Answer:
option A
Step-by-step explanation:
144 = 4 * 4 * 3 * 3 = 2 * 2 * 2 *2 * 3 * 3 = 2⁴* 3²
a¹² = a⁽³ˣ⁴⁾ = (a³)⁴
[tex]\sqrt[4]{144a^{12}b^{3}} =\sqrt[4]{2^{4}*3^{2}*(a^{3})^{4}*b^{3}}\\\\=2*a^{3}\sqrt[4]{3*3*b^{3}}\\\\=2a^{3}\sqrt[4]{9b^{3}}[/tex]