Answer:
y = 22 - x2 or x = 12 - x2
Step-by-step explanation:
what is 7x=14 show your work
Answer:
x=2
Step-by-step explanation:
7x=14
divide by 7 on each side to get x by itself
x=14/7
x=2
housing costs: a government report on housing costs says that single-family home prices nationwide are skewed to the right, with a mean of $235,700. a. we collect price data from a random sample of 50 homes in orange county, california. why is it okay to use these data for inference even though the population is skewed?
It is fine to use these data because the price sample is random so bias will not interfere with the results.
Why is it okay to use this data?Based on the information, we can infer that it is correct to use the data from this sample because it is random, that is, it does not have a defined order. Therefore, it is not necessary to take bias into account because it will not have any influence on the results.
In accordance with the above, it would be incorrect to take the data from a non-random sample because information would be prioritizing and this would cause the results to be blinded.
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Ava sells pottery at a market. Each piece of pottery costs $4.50 to make. Ava marks up the pottery by 250%. She then decides to have a sale of 30% off the retail price. What is the discounted price of each piece of pottery?
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
Explain about the discounted price?The interest rate that is adjusted to the projected cash flows of either an investment to determine its present value is referred to as the discount rate. The expected rate of return on investment that businesses or investors anticipate. The viability of an investment can be determined by computing the net present value via discounting.
Cost price = $4.50
Percentage increase = 250%.
Marked price = 4.50 + 2.5*4.50
Marked price = $15.75
Discount = 30%
Discounted price = 15.75 - 0.30*15.75
Discounted price = $11.025
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
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the anterior cruciate ligament (acl) is one of the ligaments that help stabilize the knee. surgery is often recommended if the acl is completely torn, and recovery time from the surgery can be lengthy. a medical center developed a new surgical procedure designed to reduce the average recovery time from the surgery. to test the effectiveness of the new procedure, a study was conducted in which 210 patients needing surgery to repair a torn acl were randomly assigned to receive either the standard procedure or the new procedure. (a) based on the design of the study, would a statistical
The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.
what is probability ?The study of random events or phenomena is the focus of the mathematical field of probability. It is a way to gauge how likely something is to happen. It is represented by a number between 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty. There are numerous ways to calculate probabilities, including utilizing theoretical or mathematical models, empirical data, and experimental data.
given
A statistical analysis would be useful to evaluate the effectiveness of the novel technique to the standard procedure based on the study's design.
The recovery periods of the two patient groups might be compared using statistical techniques like hypothesis testing and confidence intervals to assess the efficacy of the new therapy.
Researchers can establish whether the new approach is statistically significantly superior than the usual procedure in terms of minimizing recovery time by comparing the recovery times of the two groups.
The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.
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answer question please but DO NOT ROUND IT . 1 / 3*5 + 2
[tex]=\frac{1}{15} +2\\[/tex]
⇒We can only add the numbers if they have the same denominator, to do so we can first convert 2 into a fraction
[tex]=\frac{1}{15} +\frac{2(15)}{1(15)} \\=\frac{1}{15} +\frac{30}{15} \\=\frac{31}{15} \\[/tex]
student id numbers are created using the digits 0-9. how many five- digit student id numbers can be created if repeat digits are allowed? what if repeats are not allowed?
There are 100,000 possible five-digit student ID numbers that can be created if repeat digits are allowed (10^5).
However, if repeats are not allowed, there are only 9 x 9 x 9 x 9 x 9 = 590,490 possible student ID numbers that can be created (9^5).
The reason for the difference is that when repeats are allowed, you can use the same digit multiple times, for example "11111".
When repeats are not allowed, you can only use each digit once, for example "12345". The possible permutations of the digits 0-9 increase as more digits are added to the ID number, meaning that the more digits there are, the more possible combinations there are.
Therefore, when repeats are not allowed, the number of possible combinations is reduced significantly. In the case of five-digit student ID numbers, the difference is almost twofold.
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an oil storage tank can be described as the volume generated by revolving the area bounded by about the x-axis. find the volume of the tank (in cubic meters). round to four decimal places.
The volume of the tank can be found using the given information as:[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
How to find the volume of the tank?Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:
[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.
Therefore, the volume of the tank can be found using the given information as:
[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]
We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.
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AP Statistics Hypothesis Testing
The average amount of rainfall in the Amazon Rainforest for a year is recorded to be normally distributed with a
mean of 200 cm. Twelve regions in the Amazon Rainforest are randomly sampled. The total yearly rainfalls, in
centimeters, for these regions were reported as follows:
188 232 210 198 202. 193. 219. 202, 252, 156, 184, 222
Do this data provide sufficient evidence that the annual rainfall in the Amazon rainforest is different than 200 cm?
Therefore, based on this collection of data during a significance level of 0.05, there is insufficient proof to draw the conclusion that the average annual precipitation in the Amazonian rain forest is less than 200 cm.
What kind of hypothesis would you use?Hypothesis The amount of pleasure increases with daily solar exposure. The presumed reason in this case and the factor that is independent is sun exposure. The expected impact, or dependent variable, is the degree of happiness.
To determine if the data provide sufficient that the annual rainfall in the Amazon rainforest is different than 200 cm, we can perform a hypothesis test with the following hypotheses:
Null hypothesis: The true mean annual rainfall in the Amazon rainforest is equal to 200 cm.
Alternative hypothesis: The true mean annual rainfall in the Amazon rainforest is different than 200 cm.
We can use a two-sided t-test with a significance level of 0.05 to test this hypothesis.
We must first determine the population mean and standard variation.
x = (188 + 232 + 210 + 198 + 202 + 193 + 219 + 202 + 252 + 156 + 184 + 222)/12 = 202.17 cm
Sample standard deviation, s = 26.770 cm
Next, we can calculate the t-statistic:
t = (x - μ) / (s / sqrt(n)) = (202.17 - 200) / (26.770 / sqrt(12)) = 0.491
Using a t-distribution table with 11 degrees of freedom (n-1), at a significance level of 0.05, we find the critical values to be ±2.201. Since the calculated t-statistic of 0.491 is within the range of -2.201 to 2.201, we fail to reject the null hypothesis.
Therefore, there is not sufficient evidence to conclude that the annual rainfall in the Amazon rainforest is different than 200 cm based on this sample data at a significance level of 0.05.
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how many batteries n should be in the package in order for the probability to exceed 1%? give the smallest number n which works.
a) The probability that a battery does not reach the milestone in its first 8 hours of usage is 0.014 or 1.4%. b) The probability of this goal being met is 0.002 or 0.2%. c) The smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
(a) To calculate the probability that a battery does not reach the milestone in its first 8 hours of usage, we need to calculate the area under the normal curve to the right of 8 hours. We can use the standard normal distribution to do this by first standardizing the value of 8 hours using the formula:
z = (x - mu) / sigma
where x is the value of 8 hours, mu is the mean of the distribution (7.36 hours), and sigma is the standard deviation (0.29 hours). Substituting these values, we get:
z = (8 - 7.36) / 0.29 = 2.21
Using a standard normal table or a calculator, we can find that the area to the right of z = 2.21 is approximately 0.014.
(b) We want to find the probability that at least 10 batteries out of a pack of 12 last until 7.5 hours of usage. This is a binomial distribution with n = 12 and p = the probability that a single battery lasts until 7.5 hours.
To find p, we can use the standard normal distribution again by standardizing the value of 7.5 hours:
z = (7.5 - 7.36) / 0.29 = 0.48
Using a standard normal table or a calculator, we can find that the area to the right of z = 0.48 is approximately 0.316. Therefore, the probability that a single battery lasts until 7.5 hours is 0.316.
Now we can use the binomial distribution formula to calculate the probability that at least 10 batteries out of 12 last until 7.5 hours:
P(X >= 10) = 1 - P(X < 10)
where X is the number of batteries that last until 7.5 hours, and P(X < 10) is the cumulative probability of 9 or fewer batteries lasting until 7.5 hours. Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.998
Therefore, P(X >= 10) = 1 - 0.998 = 0.002 or 0.2%.
(c) We want to find the smallest value of n such that the probability of at least 10 batteries out of n lasting until 7.5 hours is greater than 1%. This is equivalent to finding the smallest n such that:
P(X >= 10) > 0.01
Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.989 when n = 10
P(X < 10) = 0.970 when n = 11
P(X < 10) = 0.942 when n = 12
Therefore, the smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
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Your question is incomplete, but probably the complete question is :
Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution.
(a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage.
(b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until 7.5 hours of usage. If n 12, what is the probability of this goal being met?
(c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.
a counseling service records the number of calls to their hotline for the last year. what is the forecast for august if the forecast for june was 164 and the service uses exponential smoothing with an alpha of 0.7?
Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.
Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.
The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:
St=α × Yt-1+(1-α) × St-1
where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:
St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164
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After how many weeks do you think it would be unreasonable to continue counting
individual mosquitoes? And finally, at the end of the 13-week mosquito season, how
many mosquitoes would you expect to be in the trap? Use complete sentences to
explain both of your answers below.
(Table if needed)
Week | Mosquitos
0 | 8
1 | 12
2 | 18
3 | 27
We can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.
How to determine how many mosquitoes would you expect to be in the trapBased on the given data, we can observe that the number of mosquitoes is increasing over time, and the increase is not constant. So, it would be unreasonable to continue counting individual mosquitoes after a certain point.
To estimate the number of mosquitoes at the end of the 13-week mosquito season, we can assume that the rate of increase remains constant over time. Using this assumption, we can find the average increase in mosquitoes per week, which is the difference between the number of mosquitoes in the last week and the number in the first week, divided by the number of weeks:
Average increase = (27 - 8) / 3 = 6.33
Then, we can use this average increase to estimate the number of mosquitoes in the 13th week:
Number of mosquitoes in the 13th week = 27 + 6.33 × 10 = 90.3
Since we cannot have a fraction of a mosquito, we can round this estimate to the nearest whole number.
Therefore, we can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.
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Activity 2 Synthesis
1. Precious says you can estimate the area of a circle by calculating 32. What do you think
each part of her expression means?
2. Do you agree with Precious? Use your earlier work to help support your thinking.
What is the slope of the line parallel to the function: * y = 50 -0.5x 50 0.5 -0.5 02
The slope of the line parallel to the function: y = 50 - 0.5x include the following: C. -0.5.
What are parallel lines?In Mathematics and Geometry, parallel lines simply refers to two (2) lines that are always the same or equal distance apart and never meet.
Generally speaking, two (2) lines are considered as parallel under the following standard conditions:
Slope, m₁ = Slope, m₂.
From the function, we have:
y = 50 - 0.5x
Slope, m = -0.5
In this context, we can reasonably infer and logically deduce that the slope of the two lines would be equal and the same:
Slope of line 1 = Slope of line 2
-0.5 = -0.5
In conclusion, we can logically deduce that the slope of the given line is equal to -0.5.
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simplify the following expression 4 + 4 + 4x
Answer:
Step-by-step explanation:
8+4x
each page number of a 488-page book is printed one time in the book. the first page is page 1 and the last page is page 488. when printing all of the page numbers, how many more 4's are printed than 8's?
the number of more 4's printed than 8's is 188 - 59 = 129.
We can approach this problem by counting the number of times the digit 4 appears and the number of times the digit 8 appears in the page numbers from 1 to 488.
First, let's count the number of times the digit 4 appears. We can break down the counting into three cases:
The digit 4 appears in the units place (page numbers 4, 14, 24, ..., 484): there are 49 such page numbers (from 4 to 484, incrementing by 10).
The digit 4 appears in the tens place (page numbers 40 to 49, 140 to 149, ..., 440 to 449): there are 50 such page numbers.
The digit 4 appears in the hundreds place (page numbers 400 to 488): there are 89 such page numbers.
Thus, the total number of times the digit 4 appears is 49 + 50 + 89 = 188.
Next, let's count the number of times the digit 8 appears. We can break down the counting into two cases:
The digit 8 appears in the tens place (page numbers 80 to 89, 180 to 189, ..., 480 to 489): there are 50 such page numbers.
The digit 8 appears in the hundreds place (page numbers 800 to 880): there are 9 such page numbers.
Thus, the total number of times the digit 8 appears is 50 + 9 = 59.
Therefore, the number of more 4's printed than 8's is 188 - 59 = 129.
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right cone has a base with diameter 16 units.
me volume of the cone is 320 cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base?
Answer:
The length of the segment is 8 units.
We can use the formula for the volume of a cone to calculate the height of the cone:
V = (1/3)πr^2h
320 = (1/3)π(8^2)h
h = 320/(1/3)(π)(64)
h = 8 units
In a sale, the normal price of a boat is reduced by 15%
The sale price of the boat is £272 000
Work out the normal price of the boat.
Answer:
£320 000
Step-by-step explanation:
Let x = original price of the boat.
When you reduce a price by 15%, what percent remains in the sale price?
100% - 15% = 85%
After reducing the price of the boat by 15%, the sale price is 85% of the original price.
85% of x = £272 000
0.85x = 272 000
Divide both sides by 0.85
x = 320 000
Answer: £320 000
I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:no
Step-by-step explanation:
using the Pythagorean theorem:
a^2+b^2=c^2
42^2+26^2=50^2
1764+676=2500
2440=2500
2440<2500
So the answer is no
If f(x) = 3x + 2, find f(2).
a. 2
b. 5
c. 8
d. 9
e. 12
Answer:
C
Step-by-step explanation:
Since the number in the parenthesis is treated as "x", for f(2), replace "x" with 2. So the equation will be f(2) = 3(2) + 2. Then multiply. f(2) = 6 + 2. Lastly add them up. f(2) = 8. The answer is 8.
Some of the dimensions of a house are shown below.
Calculate the length u.
Give your answer in metres to 2 d.p.
56°
1.65 m
u
43°
Not drawn accurately
Using trigonometric relations we can see that u = 4.28m
How to find the length of u?First we can find the length of the shared side using the trigonometric relation:
tan(56°) = x/1.65m
1.65m*tan(56°) = x
2.45m = x
Then the length of the bottom side of the right triangle in the right side is iven by:
tan(43°) = 2.45m/y
Solving for y:
y = 2.45m/tan(43°)
y = 2.63m
Then the length of u is:
u = 1.65m + 2.63m = 4.28m
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Mr. Salinger has 8 packs of seeds. The line plot shows the weight of each pack. Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same. What will be the weight of each pack?
Each pack should weigh 11.5 oz when the seeds are redistributed equally.
Since Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same, he needs to find the common weight of all the packs. To do this, he can find the total weight of all the packs and divide it by the number of packs.
Using the line plot, we can see that the weights of the 8 packs are:
12 oz
8 oz
10 oz
10 oz
12 oz
14 oz
10 oz
16 oz
To find the total weight of all the packs, we can add these weights together:
12 + 8 + 10 + 10 + 12 + 14 + 10 + 16 = 92 oz
So the total weight of all the packs is 92 oz.
To find the weight of each pack, we need to divide the total weight by the number of packs:
92 ÷ 8 = 11.5 oz
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I will mark BRAINLYIST
Answer:
119% of 550
Step-by-step explanation:
add the percentages
Oliver ask 20 children's how they travel to school you are other reasonOliver ask 20 children's how they travel to school here are the reason walkOliver ask 20 children's how they travel to school here are the reason what three bicycle 2 calculate the percentage of the children who travel to school by bicycle
From the given information provided, the percentage of children who travel by bicycle is 15%.
According to the given information, out of 20 children, 3 of them travel to school by bicycle. To calculate the percentage of children who travel to school by bicycle, we need to divide the number of children who travel by bicycle by the total number of children and multiply by 100.
Percentage of children who travel to school by bicycle = (Number of children who travel by bicycle / Total number of children) x 100%
= (3/20) x 100%
= 15%
Therefore, the percentage of children who travel to school by bicycle is 15%.
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find the next two terms 9.56,9.57,9.58,9,59
The next two terms in this arithmetic progression is 7.60 and 7.61.
What is arithmetic progression?An arithmetic prοgressiοn (AP) is a sequence where the differences between every twο cοnsecutive terms are the same. Fοr example, the sequence 2, 6, 10, 14, … is an arithmetic prοgressiοn (AP) because it fοllοws a pattern where each number is οbtained by adding 4 tο the previοus term. A real-life example οf an AP is the sequence fοrmed by the annual incοme οf an emplοyee whοse incοme increases by a fixed amοunt οf $5000 every year.
We know the Arithmetic progression formula:
[tex]\rm a_{n}=a_{1}+(n-1)d[/tex]
[tex]\rm a_n[/tex] = the nᵗʰ term in the sequence
[tex]\rm a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here 4 terms are given
5th and 6th terms are to be found,
Thus,
a₁ = 9.56
d = (9.56 -9.57) = 0.01
n = 5
Then
5th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (5 - 1)0.01
aₙ = 9.56 + (4)0.01
aₙ = 9.56 + 0.04
aₙ = 7.60
6th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (6 - 1)0.01
aₙ = 9.56 + (6)0.01
aₙ = 9.56 + 0.05
aₙ = 7.61
Thus, The next two terms in this arithmetic progression is 7.60 and 7.61.
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PLEASE HELP <3 Kelly walks from the 1st floor to the 5th floor. Avery walks from the 8th floor to the 4th floor. Which best describes the distance Kelly and Avery walk?
Avery walks a greater distance than Kelly.
B Kelly walks a greater distance than Avery.
C Kelly walks at a slower speed than Avery.
D Kelly and Avery walk the same distance.
Answer:
D. Kelly and Avery walk the same distance.
Step-by-step explanation:
Kelly walked from the 1st floor to the 5th floor. That means she walked 4 floors.
Avery walked from the 8th floor to the 4th floor.
8 - 4 = 4.
They walked the same distance, except Avery went down, and Kelly went up, which is unrelated.
what is the approximate probability that the actual proportion requiring aid will exceed that value? (round your answer to four decimal places.)
The approximate probability that the actual proportion requiring aid will exceed 0.08 is 0.5 (or 50%) rounded to four decimal places.
Given: The number of members in town = 400
The number of members requiring aid = 32
The proportion of members requiring aid = (number of members requiring aid) / (total number of members) = 32 / 400 = 0.08
To find the approximate probability that the actual proportion requiring aid will exceed this value, we need to assume a distribution for the proportion of members requiring aid. Assuming a normal distribution, we can use the Central Limit Theorem to approximate the sampling distribution of the sample proportion.
The standard error of the sample proportion is given by:
SE = √[p(1-p)/n]
where p is the population proportion and n is the sample size.
Substituting the values, we get:
SE = sqrt [(0.08 × 0.92) / 32] = 0.043
To find the probability that the actual proportion requiring aid will exceed 0.08, we can standardize the distribution using the z-score formula:
z = (x - p) / SE
where x is the value of the proportion we are interested in, p is the population proportion, and SE is the standard error of the sample proportion.
Substituting the values, we get:
z = (0.08 - 0.08) / 0.043 = 0
The probability that the actual proportion requiring aid will exceed 0.08 is equal to the probability of observing a z-score greater than 0, which is 0.5 (or 50%).
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The question is -
The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? .08 What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)
A square based pyramid has a base area of 25 square feet. If the
slant height forms a 50° angle with the base of the pyramid, find
the volume of the square pyramid to the nearest tenth of a cubic
foot.
Answer:
Step-by-step explanation:
square pyramid. Calculate the unknown defining height, slant height, surface area, side length and volume of a square pyrami
A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
14
6
12
4
16
Based on these results, express the probability that the next spin will land on purple
as a fraction in simplest form.
Answer:
4/13
Step-by-step explanation:
total = 14 + 6 + 12 + 4 + 16 = 52
purple = 16
p(purple) = 16/52 = 4/13
6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .
If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
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The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
Find the percentile rank for Susan who is 5th in a class of 58 students
From the given information provided, Susan's percentile rank in class is approximately 6.9%.
To find the percentile rank for Susan who is 5th in a class of 58 students, we need to use the following formula:
Percentile rank = (Number of students below Susan / Total number of students) x 100
Since Susan is the 5th student in the class, there are 4 students with higher ranks than her. Therefore, the number of students below Susan is 4.
Using the formula, we can calculate the percentile rank as:
Percentile rank = (4 / 58) x 100
Percentile rank = 6.9 (rounded to one decimal place)
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