Answer:
a. Yield
c. Pre-Order picked up
e. Pre-Orders placed.
Step-by-step explanation:
Uncertain random variables are those over which the farmer has no control. These variables are uncontrollable and there can be no prediction for it. The farmer has no control over the yield produced. He can choose what type of fruits to grow and input method but he has no control over output generated.
4g+r=2r-2x
I need someone’s help if you can help me
Answer:
4g+2x=r
Step-by-step explanation:
4g+r=2r-2x
collecting like terms
4g+2x=2r-r
4g+2x=r
Identify the sampling techniques used, and discuss potential sources of bias (if any). Assume the population of interest is the student body at a university. Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
1. What type of sampling is used?
a. Systematic sampling is used, because students are selected from a list, with a fixed interval between students on the list.
b. Cluster sampling is used because students are divided into groups, groups are chosen at random, and every student in one of those groups is sampled.
c. Simple random sampling is used because students are chosen at random.
d. Stratified sampling is used because students are divided into groups, and students are chosen at random from these groups.
e. Convenience sampling is used because students are chosen due to convenience of location.
2. What potential sources of bias are present if any. Select all that apply.
a. University students may not be representative of all people in their age group.
b. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.
c. Because of the personal nature of the question, students may not answer honestly.
d. There are no potential sources of bias.
Answer:
1. e. Convenience sampling is used because students are chosen due to convenience of location.
2. a. University students may not be representative of all people in their age group.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
Students sampled as they leave the build, which is convenience, in this case convenience of location, which means that the correct answer to question 1 is given by option e.
2. What potential sources of bias are present if any. Select all that apply.
Only members of one group are asked(university students), and this may not be representative of the rest of the population, which means that the correct answer to question 2 is given by option a.
Gsggagsgsvhdgdvdvdvdvdg help me fast I’ll give you brainliste
The answer is D
Hope that was fast enough
Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable?
Answer: a continuous random variable
Step-by-step explanation:
Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.
Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.
Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.
Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 3 + 2 cos(t), π/2 ≤ t ≤ 2π
Answer:
The motion of the particle describes an ellipse.
Step-by-step explanation:
The characteristics of the motion of the particle is derived by eliminating [tex]t[/tex] in the parametric expressions. Since both expressions are based on trigonometric functions, we proceed to use the following trigonometric identity:
[tex]\cos^{2} t + \sin^{2} t = 1[/tex] (1)
Where:
[tex]\cos t = \frac{y-3}{2}[/tex] (2)
[tex]\sin t = x - 1[/tex] (3)
By (2) and (3) in (1):
[tex]\left(\frac{y-3}{2} \right)^{2} + (x-1)^{2} = 1[/tex]
[tex]\frac{(x-1)^{2}}{1}+\frac{(y-3)^{2}}{4} = 1[/tex] (4)
The motion of the particle describes an ellipse.
Solve the system of linear equations below.
6x + 3y = 33
4x + y = 15
A.
x = 2, y = 7
B.
x = -13, y = 7
C.
x = - 2/3, y = 12 2/3
D.
x = 5, y = 1
Answer:
The answer for both linear equations is A. x = 2, y = 7
Step-by-step explanation:
First start by plugging in the variables with the given numbers (2,7). We'll start with 6x + 3y = 33.
6x + 3y = 33
6 (2) + 3 (7 )= 33 <--- This is the equation after the numbers are plugged in.
12 + 10 = 33
33 = 33 <---- This statement is true, therefore it is the correct pair.
Now we are not done, to confirm that this pair works with both equations we need to solve for 4x + y = 15 to see if it works. Linear Equations must have the variables work on both equations.
4x + y = 15 <----- We are going to do the exact same thing to this equation.
4(2) + 7 = 15
8 + 7 = 15
15 = 15 <-- 15=15 is a true statement therefore this pair works for this equation.
Therefore,
A. x = 2, y = 7 is the correct answer
Sorry this is a day late, I hope it helps.
The Blacktop Speedway is a supplier of automotive parts. Included in stock are 7 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable z represent the number that are not correctly calibrated.
Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)
x P(x)
0
1
2
3
Answer:
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
Step-by-step explanation:
The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
7 + 2 = 9 speedometers, which means that [tex]N = 9[/tex]
2 are not correctly calibrated, which means that [tex]k = 2[/tex]
3 are chosen, which means that [tex]n = 3[/tex]
Complete the probability distribution table.
Probability of each outcome.
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,9,3,2) = \frac{C_{2,0}*C_{7,3}}{C_{9,3}} = 0.4167[/tex]
[tex]P(X = 1) = h(1,9,3,2) = \frac{C_{2,1}*C_{7,2}}{C_{9,3}} = 0.5[/tex]
[tex]P(X = 2) = h(2,9,3,2) = \frac{C_{2,2}*C_{7,1}}{C_{9,3}} = 0.0833[/tex]
Only 2 defective, so [tex]P(X = 3) = 0[/tex]
Probability distribution table:
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
A six sided number cube rolled once. what is the probability of landing on a multiple of 2. write the probability as a fraction, percent and decimal.
Answer:
12 is the correct answer
If the mean, median, and mode are all equal for the set (10, 80, 70, 120, x}, find the value of x.
X
(Simplify your answer. Type an integer or a decimal.)
Question Viewer
Answer:
x=70
Step-by-step explanation:
First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.
Next, because x is the mode and has to be the median as well, and our number line so far is
(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.
Finally, to calculate the mean, we have
mean = sum / count
The mean must be x, as it is equal to the mode, so we have
x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)
multiply both sides by 5 to remove the denominator
5 * x = 10+70+80+120+x
5 * x = 280 + x
subtract x from both sides to isolate the x and the coefficient
4 * x = 280
divide both sides by 4 to get x
x= 70
We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.
I need at least two more sentences in regards with this assignment. Note the included photo. Please come up with two proper sentences following the assignments instructions. Ps. Don’t try to steal points from this or you will be reported
Answer:
A={x: x is a cat}
B={x: x likes climbing on trees}
My little cat Louis likes climbing on trees (Louis is in the intersection of the two sets)
A={x: x is a town in the USA}
B={x: x is a town in the UK}
To improve my English I'd like to go on holiday to a town in the USA, but a town in the UK would work too (the town shall be in the union of the two sets)
PLEASE ANSWER MY QUESTION AND EXPLAIN RIGHT
Answer:
$ 1943
Step-by-step explanation:
You two congruent trapezoids.
Find the area of one and multiply by 2.
A = [tex]\frac{base_{1} + base_{2} }{2}[/tex] x h
= [tex]\frac{28+39}{2}[/tex] x 14.5
= [tex]\frac{67}{2}[/tex] x 14.5
= 33.5 x 14.5
= 485.75
= 485.75 x 2 (Two trapezoids)
= 971.50
= 971.50 x 2 (two dollars a square foot)
= 1943.00
h=255-21t-16t^2
PLEASE HELP!!
Answer:
3.15 seconds is the answer.
Explanation
when the ball touches the ground, h =0
hence,
0=255-21t-16t²
16t²+21t-225=0
here a=16 ,b=21, c= -225
[tex]t= \frac{ - b± \sqrt{ {b }^{2} - 4ac} }{2a} \\ \\ t= \frac{ - 21± \sqrt{ {21}^{2} - 4 \times 16 \times - 225} }{2 \times 16} \\ = \frac{ - 21 ± \sqrt{441 - ( - 14400)} }{32} \\ = \frac{ - 21± \sqrt{14841} }{32} \\ = \frac{ - 21±121.82}{32} \\ \\ t = \frac{ - 21 + 121.82}{32} \: or \: \: t = \frac{ - 21 - 121.82}{32} \\ t = 3.15 \: \: or \: \: t = - 4.46[/tex]
time cannot be negative, hence t = -4.46 can be avoided
The ball takes 3.15 seconds to hit the ground.
Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions.
Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.)
Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.)
Answer:
For the perimeters, x must be equal to 2.
For the areas, it is either undefined, or something.
Step-by-step explanation:
You can first find the perimeters for both sides.
For the left shape, we add the two sides of 6 and x + 4 to get x + 10.
Then we multiply x + 10 by 2 because there are 4 sides, and we only got 2 sides.
The perimeter of the first shape is 2x + 20.
The second shape can be solved by doing the same thing by adding 2 and 3x + 4 to get 3x + 6.
3x + 6 times 2 is 6x + 12.
The second perimeter is 6x + 12.
If both sides are supposed to be equal, then we can write these two expressions we solved for like:
6x + 12 = 2x + 20.
Subtraction property of equality
6x + 12 - 12 = 2x + 20 - 12
Simplify
6x = 2x + 8
Again
6x - 2x = 2x - 2x + 8
Simplify
4x = 8
Division property of equality
4/4x = 8/4
Simplify
x = 2
So if x = 2, the perimeters will be the same.
You can confirm this by plugging it back into either equation.
For the areas, we just multiply the length and width for both shapes, so we get
6(x+4) = 2(3x+4)
Since they are supposed to be equal.
We simplify and get
6x + 24 = 6x + 8
We know this is false and is not possible, since we can remove the 6x because it is on both sides.
We also know that 24 is not equal to 8 (who thought!)
:D
24 ≠ 8
So it is undefined or whatever you call it.
The number of users of a certain website (in millions) from 2004 through 2011 follows:
Year Period Users (Millions)
2004 1 1
2005 2 5
2006 3 11
2007 4 58
2008 5 145
2009 6 359
2010 7 607
2011 8 846
Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast users (in millions). (Round your numerical values to one decimal place.)
Answer:
y = 26.3x² - 116.9x + 109.6
Step-by-step explanation:
Given the data ;
Year Period Users (Millions)
2004 1 1
2005 2 5
2006 3 11
2007 4 58
2008 5 145
2009 6 359
2010 7 607
2011 8 846
A quadratic regression model can be obtained using a quadratic regression calculator ; The quadratic regression modeled obtained is in the form :
y = Ax² + Bx + C
y = 26.3x² - 116.9x + 109.6
In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $2. Construct a confidence interval at a 98% confidence level.
Answer:
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 24 - 1 = 23
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 23 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.5
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.5\frac{2}{\sqrt{24}} = 1.02[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.02 = $40.98.
The upper end of the interval is the sample mean added to M. So it is 42 + 1.02 = $43.02.
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
find the value of x rounded to the nearest tenth
9514 1404 393
Answer:
3.8
Step-by-step explanation:
The angle bisector divides the triangle segments proportionally.
x/3 = 5/4
x = 15/4 = 3.75 . . . . multiply by 3
x ≈ 3.8
Mary is 3 years older than Sarah. Winifred is twice as old as Mary. Altogether their ages total 89. How old is Sarah?
24 years old
22 years old
18 years old
None of these choices are correct.
Answer:
Step-by-step explanation:
M = S+3
W = 2M = 2(S+3) = 2S+6
M+S+W = 89
(S+3)+S+(2S+6) = 89
S = 20
Answer:
20
Step-by-step explanation:
Sarah: 21
Mary: 24
Winifred: 48
No
Sarah: 20
Mary: 23
Winifred: 46
Yes
If a driver averages 50 miles per hour, the number of hours it will take to drive 360 miles is
Divide total miles by speed:
360 / 50 = 7.2 hours
Explain the difference between a rate, a ratio, and a proportion?
Answer:
A proportion is an equality of two ratios.
Example : [tex]\frac{1}{3}[/tex] = [tex]\frac{x}{9}[/tex]
We write proportions to help us find equivalent ratios and solve for unknown quantities.
A rate is the quotient of a ratio where the quantities have different units.
Example : [tex]\frac{distance}{time}[/tex]
A ratio is a comparison of two quantities.
Example : 1 : 3 or [tex]\frac{1}{3}[/tex]
Two lamps marked 100 W - 110 V and 100 W - 220 V are connected i
series across a 220 V line. What power is consumed in each lamp?
The power consumed in the lamp marked 100W - 110V is 15.68W
The power consumed in the lamp marked 100W - 220V is 62.73W
Step-by-step explanation:
Given:
First lamp rating
Power (P) = 100W
Voltage (V) = 110V
Second lamp rating
Power (P) = 100W
Voltage (V) = 220V
Source
Voltage = 220V
i. Get the resistance of each lamp.
Remember that power (P) of each of the lamps is given by the quotient of the square of their voltage ratings (V) and their resistances (R). i.e
P = [tex]\frac{V^2}{R}[/tex]
Make R subject of the formula
⇒ R = [tex]\frac{V^2}{P}[/tex] ------------------(i)
For first lamp, let the resistance be R₁. Now substitute R = R₁, V = 110V and P = 100W into equation (i)
R₁ = [tex]\frac{110^2}{100}[/tex]
R₁ = 121Ω
For second lamp, let the resistance be R₂. Now substitute R = R₂, V = 220V and P = 100W into equation (i)
R₂ = [tex]\frac{220^2}{100}[/tex]
R₂ = 484Ω
ii. Get the equivalent resistance of the resistances of the lamps.
Since the lamps are connected in series, their equivalent resistance (R) is the sum of their individual resistances. i.e
R = R₁ + R₂
R = 121 + 484
R = 605Ω
iii. Get the current flowing through each of the lamps.
Since the lamps are connected in series, then the same current flows through them. This current (I) is produced by the source voltage (V = 220V) of the line and their equivalent resistance (R = 605Ω). i.e
V = IR [From Ohm's law]
I = [tex]\frac{V}{R}[/tex]
I = [tex]\frac{220}{605}[/tex]
I = 0.36A
iv. Get the power consumed by each lamp.
From Ohm's law, the power consumed is given by;
P = I²R
Where;
I = current flowing through the lamp
R = resistance of the lamp.
For the first lamp, power consumed is given by;
P = I²R [Where I = 0.36 and R = 121Ω]
P = (0.36)² x 121
P = 15.68W
For the second lamp, power consumed is given by;
P = I²R [Where I = 0.36 and R = 484Ω]
P = (0.36)² x 484
P = 62.73W
Therefore;
The power consumed in the lamp marked 100W - 110V is 15.68W
The power consumed in the lamp marked 100W - 220V is 62.73W
One of the lengths of a leg of a right angled triangle is 15 feet. The length of the hypotenuse is 17 feet. Find the length of the other leg.
4 feet
6 feet
8 feet
10 feet
Answer:
8ft
Step-by-step explanation:
We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,
[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]
Midwest Publishing publishes textbooks. The company uses an 800 number where people can call to ask questions about the textbooks and place orders. Currently, there are 2 representatives handling inquiries. Calls occurring when both lines are in use get a busy signal. Each representative can handle 12 calls per hour. The arrival rate is 20 calls per hour.
Required:
a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
b. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used?
c. What percentage of calls receive a busy signal for the current telephone system with two extension lines?
Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
amy shoots a 100 arrows at a target each arrow with a probability 0.2 what is the probability that at most one of her first 10 arrows hits the target
Answer:
0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target
Step-by-step explanation:
For each shot, there are only two possible outcomes. Either they hit the target, or they do not. The probability of a shot hitting the target is independent of any other shot, which means that the binomial probability distribution is used to solve this 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.
Each arrow with a probability 0.2
This means that [tex]p = 0.2[/tex]
First 10 arrows
This means that [tex]n = 10[/tex]
What is the probability that at most one of her first 10 arrows hits the target?
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1074 + 0.2684 = 0.3758[/tex]
0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target
20 points help please.
Answer:
-2 is the answer trust me
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=x6, y=1 about y=6.
Answer:
mehoimehoihoi
Step-by-step explanation:
(a)234.3x13 (b) 31.38 X 5 (c) 0.653X 45 (d) 21.45X 10
(e) 25.41X 18 (f) 93.2 X 47 (g) 234.2X 342 (h) 89.4X20
(a)1.1 X 3.0 (b) 2.5 X 1.4 (c) 3.4X 4.6 (d) 2.4X4.8
(e) 2.6 X 12.3 (f) 6.72 X 56.1 (e) 24.59 X 31.2 (f) 27.15 X 3.7
what quadratic expression represents (2x+5)(7-4x)
a.-8x^2+6x-35
b.-8x^2-34x+35
c.-8x^2+34x-35
d.-8x^2-6x+35
[tex]\\\\\\[/tex]
Therefore
[tex]\sf{Option~ D ~is ~correct }[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Answer:
-8x² -6x + 35
Step-by-step explanation:
A expression is given to us and we need to find out the quadratic equation . For that Multiply the two terms of the quadratic equation. The given expression is ,
Given expression :-
[tex]\rm\implies ( 2x +5)( 7 - 4x ) [/tex]
Multiply the terms :-
[tex]\rm\implies 2x ( 7 - 4x )+5(7-4x) [/tex]
Simplifying the brackets :-
[tex]\rm\implies 14x - 8x^2 + 35 - 20x [/tex]
Rearrange and simplify :-
[tex]\rm\implies -8x^2 -6x + 35 [/tex]
Therefore :-
[tex]\rm\implies\boxed{ \rm Quadratic\ Equation \ = -8x^2 -6x + 35} [/tex]
Find the values of x and y that make these triangles congruent by the HL theorem
Answer:
x = 3, y = 2Step-by-step explanation:
As due to congruency,
x + 3 = 3y
[By putting the values of x = 3 and y = 2]
=> 3 + 3 = 3 × 2
=> 6 = 6
and,
x = y + 1
[By putting the values of x = 3 and y = 2]
=> 3 = 2 + 1
=> 3 = 3
Hence, proved
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1125. What was the rate charged per hour by each mechanic if the sum of the two rates was $140 per hour?
Answer:
The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.
Step-by-step explanation:
Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:
1125/15 = X
75 = X
80 x 10 + 60 x 5 = 800 + 300 = 1100
85 x 10 + 55 x 5 = 850 + 275 = 1125
Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.
A film distribution manager calculates that 5% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%
Answer:
0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
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]
A film distribution manager calculates that 5% of the films released are flops.
This means that [tex]p = 0.05[/tex]
Sample of 572
This means that [tex]n = 572[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.05[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{572}} = 0.0091[/tex]
What is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%?
1 subtracted by the p-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.05}{0.0091}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643
1 - 0.8643 = 0.1357
0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%