The probability that the mean of their test scores is greater than 78 is 0.0301.
Given,
Mean = 73
Standard Deviation σ = 7.8
Number of students randomly selected = 24
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.
The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The number of standard deviations from the mean is called the z - score and can be found by the formula
Z = (x - μ)/σ.
Z = (70 - 73)/(7.8/√24) = -1.88442228
P(z < -1.88) = 0.0301
Therefore, P(z < -1.88) = 0.0301
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 170 engines and the mean pressure was 7.7 lbs/square inch. assume the standard deviation is known to be 0.8. if the valve was designed to produce a mean pressure of 7.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
The null hypothesis is that the mean is equal to 7.6 lbs while the alternate hypothesis of the valve is that it is not equal to 7.6lbs.
What is a Hypothesis in statistics?
This term is used to refer to a statement which is made that is tested to be true or untrue during the study.
The Null hypothesis
H0: μ = 7.6
The alternate hypothesis:
H1: μ ≠ 7.6
The null hypothesis says the valve produces a mean pressure of 7.6 lbs. The alternate hypothesis on the other hand says that it does not equal to 7.6lbs.
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Answer:
H0: μ=7.6
Ha: μ>7.6
question 2 a supervisor asks a junior data analyst to present two hypotheses regarding a data analytics project. what is the purpose of a hypothesis?
Making predictions about your data requires the usage of a hypothesis. They aid data analysts in determining what they want to verify or dispute.
Given,
A senior data analyst requests that a junior data analyst offer two hypotheses for a project involving data analytics.
The rationale for a hypothesis must be explained;
This is,
Hypothesis testing is a sort of statistical reasoning that uses information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially best guessed.
Here,
A hypothesis seeks to infer something from your data. Data analysts use them to show or refute what they want to prove.
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The radius of a circular disk is given as 27 cm with a maximum error in measurement of 0.2 cm.
1) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.)
2)What is the relative error? (Round your answer to four decimal places.)
3)What is the percentage error? (Round your answer to two decimal places.)
The maximum error in the area is 33.933 sq cm. The relative error is 0.0148. The percent error will be 1.48%.
What is area?The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
1) A = pi(r²)
dA = 2(pi)r(dr)
= 2(3.14)(27)(0.2) sq cm
= 33.93 sq. cm
2) Relative error is the above divided by actual area
actual area=3.14*27*27
=2289.06 sq cm
Relative error=0.0148
3) % error -- convert the above to a % by appropriate shifting of decimal point
% error=0.0148*100
=1.48%
The area's largest inaccuracy is 33.933 sq cm. 0.0148 is the relative inaccuracy. There will be a 1.48% error percentage.
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I NEED DESPERATE HELP PLEASE 25x^2-17+-1
solve
Round the decimal 213.21 to the nearest whole number.
Answer: 213
Step-by-step explanation:
Answer: 213
Step-by-step explanation:
(a) at point a or point b is the gradient vector more horizontal? why? (b) at point a or point b is the gradient vector longer? why?
The definition of the gradient vector for point a to b is defined below.
Vector:
In math vector value consists of magnitude and direction.
Given,
Here we need to find the gradient vector of point a or point b.
According to the definition of vector, a multidimensional input have partial derivatives, you might wonder what the full derivative of such a function is. Here in the case of scalar-valued multivariable functions, meaning those with a multidimensional input but a one-dimensional output, the answer is the gradient.
Where as the gradient of a function f, denoted as ∇f,
Where f, is the collection of all its partial derivatives into a vector.
Here the point a and b is more horizontal because of the partial derivative nature of vector.
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madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random. what are the odds in favor of her selecting a red marble? (type answer in form a:b) 5:30
The odds in favor of her selecting a red marble = 6/7
Here, Madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random.
We need to decide the odds in favor of her selecting a red marble.
Total number of marbles = 30 + 5
Total number of marbles = 35
So, the odds in favor of her selecting a red marble would be,
p = number of favourable outcomes / total number of outcomes
p = 30/35
p = 6/7
Therefore, the probability that she select a red marble is 6/7
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28 Find the area of the figure below.
2(2x-4)om
(2x+10) cm
A. 528cm²
C. 480cm²
B. 92cm²
D. 46cm²
(x +13)cm
*
35
Answer:
A=L*W2x-4=2x+10x=14ans=912Will mark brainliest. Question’s below! Please! Thank you!
Answer:
x = -2, y = -3
Step-by-step explanation:
Solve for y:
If -3x + 9y = -21, and -3x +8y = -18, then -21 - y = -18
Add 18 to both sides:
-3 - y = 0, so y = -3
reconstruct new equation:
-3x + 9(-3) = -21, -3x + 8(-3) = -18
-3x + -27 = -21, -3x + -24 = -18
Using the new equation, solve for x:
add 24 to both sides of each equation :
-3x + -3 = 3, -3x = 6
x=-2
consider the following binomial experiment: the probability that a cell phone manufactured at electronics unlimited is defective is 0.11. if a sample of 6 cell phones is selected at random, what is the probability that at least one is defective? a) 0.4423 b) 0.5030 c) 0.4970 d) 0.5584 e) 0.4416 f) none of the above.
Using the binomial distribution, it is found that there is a 0.5954 = 59.54% probability that at least 1 is defective.
What is the binomial distribution?
A collection of numerous independently distributed Bernoulli trials with equal distributions results in the binomial distribution. The experiment in a Bernoulli trial is said to be random and can only result in one of two outcomes: success or failure.
For each phone, there are only two possible outcomes, either it is defective, or it is not. The probability of a phone being defective is independent of any other phone, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex]
[tex]C_n, x = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of success on a single trial.
In this problem:
0.11 probability of a single phone is defective, hence
6 phones are selected at random, hence
The probability that at least 1 is defective is:
P(X >= 1) = 1 - P(X = 0)
In which
[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex].
P(x = 0) = C₆,₀.(0.11)⁰ (0.86)⁶ = 0.4046
Then:
P(X >= 1) = 1 - P(X = 0) = 1 - 0.4046 = 0.5954
Hence, the 0.5954 = 59.54% probability that at least 1 is defective.
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What is the area of triangle ABC if a = 7, c = 11, and B = 55°?
Round the answer to the nearest hundredth.
The area of the triangle is 31.54 square units
How to determine the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
We have the following values
a = 7 units
c = 11 units
B = 55 degrees
The area of the triangle is calculated using the following area formula
Area = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 7 * 11 * sin(55 degrees)
Evaluate
Area = 31.54
Hence, the area is 31.54 square units
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PLEASE HELP ASAP!!!!
Answer:
11.3
Step-by-step explanation:
Angles A & B are each 45 degrees because if you subtract 90 from 180 and divide that by 2 you get 45 then you do:
sin(45) times 16 which is 11.3
SIN = opposite over hypotenuse.
1400 people signed up for a bike sharing program. This represents 8% of the people who live in Divyas town. 75% of the people who signed up for the program also own cars.
Answer:
what is the question??????
You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program and the thirst received usual heart care from their personal physicians. In the next three years, only three of the 33 people in the stress management group suffered "cardiac events", defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34 people in the exercise group and 12 out of the 40 patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. What are the success rates of the three treatments in preventing cardiac events?
c. Find the expected cell counts under the null hypothesis that there is no difference among the treatments. Verify that the expected counts meet the guidelines for use of the chi-square test.
d. Is there a significant difference among the success rates for the three treatments?
e. Write a brief summary that includes the test results and also percentages that compare the success of the two treatments.
a)The two way table is shown in figure,
b)The success rate of the three treatments in preventing cardiac arrests are 90.91% , 79.41% and 70%.
c)The expected cell count are as shown in the figure,
d)No. There is no difference among the treatments.
e) The brief summary is mentioned below.
Given,
The total number of people is 107.
33 people are enrolled in a stress management programme.
3 people had cardiac events as a result of the stress management programme.
34 people are in the exercise group.
The number of cardiac events in the exercise group was 7 people.
40 people receive routine care.
12 people had cardiac events while receiving standard care.
a)
The two-way table for the given information is shown in the figure
b)
During the same time period, 7 of the 34 people in the exercise group and 12 of the 40 patients in usual care experienced such events.Success rate can be determined by,
[tex]Success=\frac{no.\ of\ people\ who\ did not\ suffered\ in\ group}{Total\ number\ of people\ in\ group}[/tex]
For stress management:-
[tex]Success\ rate = \frac{30}{33}=0.9091=90.90\%[/tex]
For exercise program:-
[tex]Success\ rate = \frac{27}{34}=0.7941=79.41\%[/tex]
For usual care:-
[tex]Success\ rate = \frac{28}{40}=0.7=70\%[/tex]
c)
Expected cell count can be calculated by formula,
[tex]Expected\ value=\frac{row\ total*column\ total}{table\ total}[/tex]
then,
Expected value for the people who suffered cardiac arrest,
Under stress management:-
[tex]E= \frac{22*23}{107}=6.79[/tex]
Under exercise group:-
[tex]E=\frac{22*34}{107}=6.99[/tex]
Under usual care:-
[tex]E=\frac{22*40}{107}=8.22[/tex]
Expected value for the people who did not suffered cardiac arrest :-
Under stress management:-
[tex]E=\frac{85*33}{107}=26.21[/tex]
Under exercise group:-
[tex]E=\frac{85*34}{107}=27.01[/tex]
Under usual care:-
[tex]E=\frac{85*40}{107}=31.78[/tex]
The expected cell count is mentioned in the table
d)
The null and alternate hypothesis are
[tex]H_0[/tex] :There is no difference in the actual success rates of the three treatments.
[tex]H_1[/tex] :The three treatments differ in terms of actual success rates.
The test statistic can be calculated by
[tex]x^2=\sum \frac{(O-E)^2}{E}[/tex]
Where,
O=observed value
E=Expected value
Under null hypothesis,
[tex]x^2=\frac{(3-.679)^2}{6.79}+\frac{(7-6.99)^2}{6.99}+\frac{(12-8.22)^2}{8.22}+\frac{(30-26.21)^2}{26.21}+\frac{(27-27.01)^2}{27.01}+\frac{(28-31.78)^2}{31.78}\\\\=4.8514[/tex]
The p-value for the test is [tex]P(x_2 > 4.8514)=0.0884[/tex]
There is no statistically significant difference in the success rates of the three treatments.
e)
Because the p-value is greater than 0.05 (at the 5% level of significance), there is insufficient evidence to reject the null hypothesis and conclude that there is no difference in the actual success rates for the treatments.
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To prepare for the drama club's upcoming musical performance, Ms. Melody is printing programs on the school's copier. The number of programs Ms. Melody has printed increases over time. This situation can be modeled as a linear relationship.
What does the slope of the line tell you about the situation?
The slope of linear graph is 4 which means the rate of prinitng program copies is 4 copies per minute.
What is formula for slope?
The slope of the line between two points (x₁, y₁) and (x₂, y₂) is
m = (y₂ - y₁)/(x₂ - x₁)
Slope of a line signifies rate of change between two quantities.
According to the given question:
(Check the graph attached below)
From the graph the two points we can consider for finding the graph are (0,0) and (3, 120)
Putting these values in the formula for slope
m = (y₂ - y₁)/(x₂ - x₁)
= (120 -0)/(30 - 0)
= 4
Hence slope of the line in the situation tells that the rate of printing program is 4 copies per minute.
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1. Which number has an absolute value greater than 8?
a) 9
b) -8
c) 0
d) 8
Answer:
b)-8
Step-by-step explanation:
Because the absolute value of -8 is 8 and it will have an greater number then all of them
question content area top part 1 a pair of dice is rolled. what is the probability of getting a sum less than 5?
When a pair of dice is rolled, there is a 1/6 chance that the result will be less than 5.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Here,
Total possibility=36
To calculate the probability correctly, the list should be,
(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)
Total cases=6
probability of getting a sum less than 5,
=6/36
=1/6
The probability of getting a sum less than 5 when a pair of dice is rolled will be 1/6.
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find the distance between the two points (7,4) (3,3)
Applying the distance formula, the distance between the two points (7, 4) and (3, 3) is: 4 units.
How to Find the Distance Between Two Points?If we have two given points with their coordinates, to find the distance between these two points, apply the distance formula that is expressed as:
d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Given the two points:
(7, 3) = [tex](x_1, y_1)[/tex]
(3, 3) = [tex](x_2, y_2)[/tex]
Substitute the values into the distance formula:
d = √[(3−7)² + (3−3)²]
d = √[(−4)² + (0)²]
d = √16
d = 4 units.
The distance is: 4 units.
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only six and seven needed
6- G and P are collinear
7- Points D,H and P are collinear
Answer: 67 87 34
Step-by-step explanation:
I can’t figure this out!
Each candy costs $3 and each pretzel costs $4.25
Calculating the cost of candies and pretzelsFrom the question, we are to determine the price of each candy and the price of each pretzel
Let the price of each candy be x and the price of each pretzel be y
From the given information,
3 candies and 2 pretzels cost $17.50
Then, we can write that
3x + 2y = 17.50 ----------- (1)
Also,
9 candies and 4 pretzels cost $44
Then,
9x + 4y = 44 ------------ (2)
Solve the equations simultaneously
Multiply equation (1) by 2 and subtract it from equation (2)
2 × [3x + 2y = 17.50
6x + 4y = 35
Subtract from equation (2)
9x + 4y = 44
- [6x + 4y = 35
---------------------------------
3x + 0 = 9
3x = 9
Divide both sides by 3
3x/3 = 9/3
x = 3
substitute the value of x into equation (2)
9x + 4y = 44
9(3) + 4y = 44
27 + 4y = 44
4y = 44 - 27
4y = 17
y = 17/4
y = 4.25
Hence, the cost of the candy is $3 and the cost of the pretzel is $4.25
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In PQR, QR PQ and m/Q = 159°. Find m/P.
Applying the definition of an isosceles triangle, the measure of angle P = 10.5°.
What is an Isosceles Triangle?If a triangle has two sides that are of the same length, then the triangle is an isosceles triangle. Thus, the angles that are opposite the two equal sides of an isosceles triangle are called the base angles, and they are therefore congruent to each other.
Given that triangle PQR has two equal sides, QR ≅ PQ, it means it is an isosceles triangle, therefore its base angles, ∠P ≅ ∠R.
Therefore:
m∠Q = 159° [given]
m∠P = 1/2(180 - 159)
m∠P = 1/2(21)
m∠P = 10.5°
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4800 people attended a football game. If 10% of the people who attended were teenagers, how many teenagers attended the game?
Answer: 480 are teenagers
Step-by-step explanation:
To find a percentage of a number, I like to convert the percentage into its decimal form, so I do...
10% = .1 because a percentage is out of a whole number. 100% = 1.
Next, multiply your sum by the percentage you are looking for, so...
[tex]4800*.1=480[/tex]
How many eighty-fours are in 672?
Answer: 8
Step-by-step explanation:
We only need to take 672/84 = 8
So there are 8
If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer:
x=8
Step-by-step explanation:
Lets assume that the number of 84 is x
as given in this equation
total values given in the question be 672
then the equatiuon becomes
84 multiplied by x is 672
simplify above the equation
84x=672
[tex]x=\frac{62}{84}[/tex]
x=8
Therefore, the number of 84 is 672 is 8.
(Hope this helped! :D)
a population of protozoa develops with a constant relative growth rate of 0.8603 per member per day. on day zero the population consists of four members. find the population size after four days. (round your answer to the nearest whole number.)
The population size after four days is 121.
Given that,
a population of protozoa with a constant relative growth rate of 0.8603 per member per day
let P be the population size and let t be the time interval then the given system modeled by the differential equation
[tex]\frac{dP}{dt}[/tex] = 0.8603
by solving the separable equation and expifying both sides we get,
P = A [tex]e^{0.8603t}[/tex]
From the condition that on day zero the population consist of four members,
i.e. P(0) = 4, A = 4
Therefore population size after four days is
P(4) = 4[tex]e^{4(0.8603)}[/tex]
= 4 [tex]e^{3.441}[/tex]
= 4 × 30.295
P(4) = 121.2
nearest whole number is 121
i.e P(4) = 121
Hence the population size after four days is 121.
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You are planning a cookout and figure that you will need at least 3 packages of hot dogs and hamburgers. A package of hot dogs, x, costs $4 and a package of hamburgers, y, costs $5. You can spend a maximum of $20 on hot dogs and hamburgers.
a. Write a system of linear inequalities for the number of packages of each that can be bought.
A system of linear inequalities for the number of packages of both hot dogs and hamburgers that can be bought is as follows:
x + y ≥ 3.
4x + 5y ≤ 20.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of hot dogs.Let the variable y represent the number of packages of hamburgers.Since you will need at least 3 packages of both hot dogs and hamburgers, the linear inequality to represent this is as follows:
x + y ≥ 3.
For the cost of both hot dogs and hamburgers, and the maximum amount you can spend;
4x + 5y ≤ 20.
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a portfolio has a 3-year standard deviation of 18.1%. what is the 1-year standard deviation? group of answer choices 8.69% 11.80% 10.45% 6.39%
The one - year standard deviation is, 10.45%.
what is standard deviation?
The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.
Given:
A portfolio has a 3-year standard deviation of 18.1%.
We have to find the one - year standard deviation.
One - year SD = Variance / number of years.
Here,
Variance = square of standard deviation = (18.1)^2 = 327.61
So,
One - year SD = 327.61 / (3/1)
One - year SD = 109.20
Now,
(109.2)^(1/2) = 10.45%
Hence, the one - year standard deviation is, 10.45%.
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FAST
If Gabriel has 25.65 kg an he sold 3.87 how many kg he has?
Correct answer gets a Brainliest and 5 stars.
Answer: 21.78
Step-by-step explanation:
25.65 - 3.87 = 21.78
Write x^5/x^7 as a single exponential expression
Answer:
Usually we write the final answer with positive exponents.
[tex]\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{x^{5} }{x^{7} }[/tex]
When we are dividing powers with the same bases, we subtract the exponents.
[tex]x^{5-7}[/tex] = [tex]x^{-2}[/tex] or [tex]\frac{1}{x^{2} }[/tex]
y normally distributed with a standard deviation of 40 hours. how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of 68 is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean for the standard deviation of 40 hours
Since a level =1-0.96/2 =0.02, here the Z value of 1-a = 1-0.02= 0.98 , for which z=2.055 .Now we know that the formula for margin is:
M = z*σ/√n, where σ is the standard deviation and n is the sample size since we are provided with the standard deviation of 40 and M=10. so,
=> 10= 2.055*40/√n
=>10√n= 2.055*40
=>√n = 82.2/10
=>n=67.6 ,which is almost 68
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Point T is located at (-6, -2) on the coordinate plane. Point T is reflected over the
y-axis to create point T'. What ordered pair describes the location of T'?
Answer:
(6,-2)
Step-by-step explanation:
The point is now 6 units to the right of the y axis. That would be 6, but the y value would be the same 2 units below the x axis.