Answer: the average speed of the runners increased since last year.
Step-by-step explanation:
The table is:
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Looking at this table we can see that this year, the mean time is smaller than the one from last year, so the runners are faster in average.
The mean absolute deviation is bigger, but the change in the mean is bigger.
difference of the mean 16.2 - 14.7 = 1.5
difference of the MAD 1.9 - 1.2 = 0.7
This means that the average speed of the runners increased since last year, and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike like last year.
Answer:
this guy above me is a genuies it correct
Step-by-step explanation:
hernando is choosing a random number between 0 and 9 state the number of successful outcomes for choosing an even number
There are five successful outcomes for choosing an even number between 0 and 9, which are 0, 2, 4, 6, and 8.
Hernando is choosing a random number between 0 and 9. The even numbers in this range are 0, 2, 4, 6, and 8. To determine the number of successful outcomes for choosing an even number, we simply count the even numbers listed.
There are five even numbers between 0 and 9 which are: 0, 2, 4, 6, and 8. Therefore, there are five successful outcomes for choosing an even number.
Carla has a list of all 720 students in her middle school. She writes the name of each student on a slip of paper and puts each slip in a box. Then she pulls out 30 names from the box to decide who she will survey about the upcoming school election. How many students are in Carla's Sample?
Answer:
Step-by-step explanation:
Given that,
Clara has a list of 720 names
She decided to survey 30 names from the sample.
It is very straight forward, there are 30 names in Clara sample
But this sample can be use to generalize the overall population of 720 students if they are given equal chances of being selected maybe by taking a survey or picking their names randomly from a box
If it not a biased sample then we can use the survey to generalized the overall population
So, there are 720 names in Clara's sample
Ben has a square garden that has sides measuring X feet, Ben wants to increase every side of his garden by 11 feet in order to plant more vegetables after Ben increased his garden it will have a perimeter of 104 feet, write an equation that can use the find X
We have been given that Ben has a square garden that has sides measuring X feet, Ben wants to increase every side of his garden by 11 feet in order to plant more vegetables. So each side of garden would be [tex]X+11[/tex].
We are also told that after Ben increased his garden it will have a perimeter of 104 feet.
We know that perimeter of square is 4 times the side length. So perimeter of garden after enlargement would be [tex]4(X+11)[/tex].
Now we will equate perimeter of new garden with 104 as:
[tex]4(X+11)=104[/tex]
Therefore, the equation [tex]4(X+11)=104[/tex] can be used to solve for X.
[tex]\frac{4(X+11)}{4}=\frac{104}{4}[/tex]
[tex]X+11=26[/tex]
[tex]X+11-11=26-11[/tex]
[tex]X=15[/tex]
Therefore, the value of X is 15 feet.
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses. H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05. Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
What assumption about the sample underlies the hypothesis test?
a.The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.
b.The sample comes from a population of tires with 60,000 miles where 3.6% of the tires are worn out.
c.The sample comes from a population of tires where 250 are used for 60,000 miles.
d.The sample comes from a population of 250 tires that have a 60,000 mile warranty.
Answer:
(A)The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.
Step-by-step explanation:
The tire manufacturer has a 60,000 mile warranty for tread life. To verify the authenticity of its claim, it picks a sample of 250 tires (out of the population of tires) that have been used for 60,000 miles.
Given the hypothesis:
[tex]H_0[/tex]: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
[tex]H_a[/tex]: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
It is assumed that 5% of the tires in the sample are worn out and the hypothesis is formulated to prove or disprove this assumption.
The Federal Pell Grant Program gives grants to low-income undergraduate students. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. We wonder if the mean amount is different this year for Pell grant recipients at San Jose State University. Suppose that we randomly select 50 Pell grant recipients from San Jose State University. For these 50 students, the mean Pell grant award is $2,450 with a standard deviation of $600. Let μ = the mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year. We test the following hypotheses. H 0: μ = 2600 H a: μ ≠ 2600 The sample size is greater than 30, so a t-model is a good fit for the sampling distribution. Use this information to answer the next two questions. Flag this Question Question 12.5 pts What is the t-test statistic? If necessary, round to two decimal places.
Answer: the t-test statistic is - 1.77
Step-by-step explanation:
For the null hypothesis,
H 0: μ = 2600
For the alternative hypothesis,
H a: μ ≠ 2600
This is a two tailed test
Since no population standard deviation is given, the distribution is a student's t.
Since n = 50,
Degrees of freedom, df = n - 1 = 50 - 1 = 49
t = (x - µ)/(s/√n)
Where
x = sample mean = $2450
µ = population mean = $2600
s = samples standard deviation = $600
Therefore,
t = (2450 - 2600)/(600/√50) = - 1.77
The t-test statistic calculated for the given data comparing the mean Pell grant award at San Jose State University to the national average for 2007-2008 is approximately -1.77.
Explanation:The t-test statistic is calculated using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(sample size)). In this case, the sample mean is the mean Pell grant award for the 50 students from San Jose State University ($2,450), the population mean is the average Pell grant award according to the National Postsecondary Student Aid Study for 2007-2008 ($2,600), the standard deviation is $600, and the sample size is 50. Substitute these values into the formula to get: t = ($2,450 - $2,600) / ($600 / sqrt(50)) = -$150 / ($600 / 7.071) = -$150 / 84.85 = -1.77. So the t-test statistic is approximately -1.77, comparing the mean Pell grant award at San Jose State University to the national average for 2007-2008.
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What is the name of an angle that is formed by one side of an triangle and the extension of an adjacent side?
Answer:
an exterior angle is the correct answer.....
Answer:
A
Step-by-step explanation:
Rearrange this to make a the subject
Answer:
[tex]a = \frac{w + 4 - 3b}{6} [/tex]
Step-by-step explanation:
[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b}{6} = \frac{6a}{6} \\ a = \frac{w + 4 - 3b}{6} [/tex]
Thanks
hope this helps!!
I'd appreciate if you rate my answer and give a thanks.
Make y the subject of the formula
Step-by-step explanation:
[tex]hi \: your \: answer \: is \: d \\ w = {x}^{2} - 2yz \\ w - {x }^{2} = - 2yz \\ 2yz = {x }^{2} - w \\ divide \: both \: sides \: by \: 2z \\ y = \frac{ {x}^{2} - w }{2z} [/tex]
Answer:
Answer B
[tex]y = \frac{w - {x}^{2} }{2z} [/tex]
Step-by-step explanation:
[tex]w = {x}^{2} - 2yz \\ w - {x}^{2} = 2yz \\ \frac{w - {x}^{2} }{2z} = \frac{2zy}{2z} \\ \\ y = \frac{w - {x}^{2} }{2z} [/tex]
thanks
hope this helps
I'd appreciate if you rate my answer and give a thanks.
A rhino can run at speeds of about 28 miles per hour. What is that speed in
feet per second, to the nearest whole number? (Remember, there are 5280
feet in a mile, 60 seconds in a minute, and 60 minutes in an hour.)
A. 189 feet per second
B. 41 feet per second
C. 88 feet per second
D. 36 feet per second
Given:
A rhino runs at a speed of about 28 miles per hour.
We need to determine the speed in feet per second.
Converting miles to feet:
The miles can be converted to feet by multiplying 5280 with 28 miles per hour.
Thus, we have;
[tex]28\times 5280=147840[/tex]
Thus, the speed of the rhino in feet per hour is 147840
Converting hours to seconds:
The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)
Thus, we get;
[tex]Speed=\frac{147840}{3600}[/tex]
[tex]Speed = 41.066667[/tex]
Rounding off to the nearest whole number, we get;
[tex]Speed =41[/tex]
Therefore, the speed of the rhino is 41 feet per second.
Hence, Option B is the correct answer.
A publisher reports that 53%53% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250250 found that 44%44% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
[tex]z=\frac{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/tex]
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
Step-by-step explanation:
Data given and notation
n=250 represent the random sample taken
[tex]\hat p=0.44[/tex] estimated proportion of of the readers owned a particular make of car.
[tex]p_o=0.53[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true porportion is equal to 0.53.:
Null hypothesis:[tex]p=0.53[/tex]
Alternative hypothesis:[tex]p \neq 0.53[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
which statement best describes the interquartile range of set of weights
120 115 135 105 80 160
Answer:
The IQR is 30
Step-by-step explanation:
Answer: the difference between the second and fifth element of the set after it has been ordered from least to greatest (D)
Step-by-step explanation: I just finished the quiz and got It correct
Compute the triple integral of f(x, y, z) = z over the region F below the sphere x2 + y2 + z2 = 8 and above the triangular region in the xy-plane bounded by x = 0, y = 2, and y = x.
I suppose "below the sphere" means "inside" it, or below the upper half of it. The integral is
[tex]\displaystyle\iiint_Fz\,\mathrm dV[/tex]
where
[tex]F=\{(x,y,z)\mid0\le x\le2,x\le y\le2,0\le z\le\sqrt{8-x^2-y^2}\}[/tex]
Evaluating the integral in Cartesian coordinates is straightforward enough to not require changing coordinates:
[tex]\displaystyle\int_0^2\int_x^2\int_0^{\sqrt{8-x^2-y^2}}z\,\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle\frac12\int_0^2\int_x^2(8-x^2-y^2)\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle\frac12\int_0^2\left(16-8x-2x^2+\frac{4x^3-8}3\right)\,\mathrm dx=\boxed{\frac{16}3}[/tex]
The problem involves calculating a triple integral of a function over a specified region. The function is transformed into spherical coordinates considering the given boundaries. Afterwards, we solve the triple integral by integrating with respect to the spherical coordinates.
Explanation:The given function in the question you're asking about belongs to triple integration, a concept in calculus that extends the idea of one-dimensional integration to three dimensions. In the context of the problem, your function, f(x, y, z) = z, is defined over the region F below the sphere x2 + y2 + z2 = 8 and above the triangular region in the xy-plane bounded by x = 0, y = 2, and y = x.
Firstly, let's convert the coordinates to spherical coordinates. This is appropriate especially when dealing with volumes of spheres or parts of spheres. If we translate these conditions into spherical coordinates, where:
x = ρsinφcosθy = ρsinφsinθz = ρcosφThe triple integral thus becomes:
∫02π∫0π/4∫02 ρcosϕ * ρ2sinϕ dρ dϕ dθ.
Note that ρ2sinϕ in the equation above is the Jacobian determinant that arises from the transformation to spherical coordinates. Proceed to solve the triple integral above by integrating with respect to ρ, then ϕ, and finally θ.
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Ronique recorded the number of games that the school softball team won each year for the past 7 years: 31, 24, 32, 22, 34, 28, 38. Ronique's team won at least
games in 75% of the seasons that they played.
Answer:
156
Step-by-step explanation:
Total number of games played by Ronique's team is ≤ 279(round off).
What is at least?
" At least represents the minimum quantity of the number . it can be more than the given condition."
According to the question,
Number of games team won each year for the past 7 years are
31, 24, 32, 22, 34, 28, 38.
Total number of games won by team = 31 + 24 + 32+22 + 34 + 28 + 38
= 209
Team won at least 75% of the seasons they played
'x' represents the total number of seasons they played
Therefore,
75% of x ≤ 209
⇒[tex]\frac{75}{100} (x)\leq 209[/tex]
⇒ [tex]x \leq \frac{(209)(100)}{75}[/tex]
⇒ [tex]x\leq 278.666..[/tex]
⇒[tex]x\leq 279 (round off)[/tex]
Hence, total number of games played by Ronique's team is ≤ 279(round off).
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Varios estudiantes de una escuela pintaron 15 pancartas en 3 horas. Cuantas horas les tomará a los estudiantes pintar 60 pancartas
Answer:
The time it will take to paint 60 banners is 12 hours.
Step-by-step explanation:
The question is:
Several students from one school painted 15 banners in 3 hours. How many hours will it take for students to paint 60 banners
Solution:
The Unitary method is a mathematical procedure to determine the value of 1 unit from n unit values.
It is provided that the time it takes to paint 15 banners is, t = 3 hours.
Then the time it should have taken to paint 1 banner is, [tex]\frac{3}{15}=\frac{1}{5}\ hours[/tex].
Compute the time it will take to paint 60 banners as follows:
Time = [tex]60\times \frac{1}{5}=12[/tex]
Thus, the time it will take to paint 60 banners is 12 hours.
75% of b is 12. What is b
Answer:
B=16
Step-by-step explanation:
If 75% is 12, 100% would be 16. B = 16!
Answer:16
Step-by-step explanation:
12/3=4 4=25%of b 4+12=16
Theo solved n + 5 = 11 for the unknown. The steps he
took are shown.
He started with 5 tiles.
Then he added tiles as he counted up to 11.
He realized he added 6 more tiles to his original 5 to make
11. So he found the unknown to be 6.
Answer:
what is the question?
Step-by-step explanation:
Solve for x; X/3 = 2/9
Step-by-step explanation:
x/ 3 = 2 / 9
Cross multiply
9x = 6
x = 6 / 9
x = 2 / 3
Need help with this geometry
4. Each item produced by a certain manufacturer is, independently, of acceptable quality with probability 0.95. Suppose that we want to approximate the probability that at most 10 of the next 150 items produced are unacceptable. a) Approach this using the normal approximation to the binomial distribution. Make sure to provide a z-score and a probability with four decimal places. b) Use either R or the Excel BINOM.DIST function to find the exact probability.
Answer:
Step-by-step explanation:
This one is really hard I cannot
Calculate the perimeter of this shape.
10 cm
19 cm
Answer:
Depending on the exact measurements of the sides, the way to find perimeter would be to add up all the measurements along the sides. If this shape were only two sides, which is impossible, the perimeter would be 10 + 19, or 29.
Step-by-step explanation:
Answer:
you have to stretch the shape out and then add them
Step-by-step explanation:
so 10+19+10+19=58
An equilateral triangular plate with sides 10 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
1225000
Step-by-step explanation:
The hydrostatic force against one side of the submerged equilateral triangle can be obtained by integrating the product of the fluid pressure and the area of an infinitesimally small strip on the triangle from base to top, yielding a result of 49,000 Newton.
Explanation:To express the hydrostatic force against one side of the equilateral triangular plate as an integral, we need to start with the equation for the pressure at any point in a fluid: P = ρgh. This is the product of the water density (ρ), gravitational acceleration (g), and height inside the fluid (h).
Next, we multiply this by the area of an infinitesimally small horizontal strip on our triangular plate, and then integrate to account for the entire side of the triangle, from the base to the top. In this problem, the area of the strip depends on the height, and for an equilateral triangle with a side length of 10m, it can be expressed as 10-2y.
Therefore, the hydrostatic force F becomes the integral ∫(0 to 10) ρg(10 - y)dy, where ρ is the weight density of water 1000 kg/m3, g stands for the acceleration due to gravity 9.8 m/s2, and y is the height varying from 0 to 10 m. Evaluating this integral, we get F = 49,000 Newton.
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what is the distance between 120 and -150 on a number line
Answer:
[tex]270[/tex]
Step-by-step explanation:
[tex]120 - ( - 150) \\ 120 + 150 \\ = 270[/tex]
The distance between 120 and -150 on a number line is calculated by subtracting the smaller number from the larger number. Given that -150 is negative, the subtraction turns into addition, leading to a distance of 270.
Explanation:To find the distance between 120 and -150 on a number line, you need to take the following steps:
Identify the two points on the number line. In this case, they are 120 and -150.Subtract the smaller number from the larger one. Since 120 is greater than -150, you subtract -150 from 120.However, since -150 is a negative number, when you subtract it, it becomes addition. So the calculation becomes 120 + 150.The result will be the distance between the two numbers, which is 270.Therefore, the distance between 120 and -150 on a number line is 270
.
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Gas prices went up this week from $4.00 a gallon to $4.20. what is the percent increase of the price?
A couple plans to have three children. Each child is equally likely to be a girl or boy, with gender independent of that of the other children. a. Construct a sample space for the genders of the children, using B for boy and G for girl. b. Find the probability that all 3 of the children are boys. c. Answer part b if, in reality, for a given child, the chance of a boy is 0.51.
Answer:
a) X={BBB;BBG:BGG:GGG}
b) P(BBB)=0.125
c) P(BBB)=0.133
Step-by-step explanation:
The sample space states all the possible values that the random variable can take. In this case, the order does not matter, so the possible combinations for the random variable are:
X={BBB;BBG:BGG:GGG}
The probability p of having a boy is p=0.5, as it is equally likely to have a girl or a boy.
The probability that all 3 children are boys can be calculated multiplying 3 times the probability of having a boy. That is:
[tex]P(X=BBB)=p\cdot p\cdot \cdot p =p^3=0.5^3=0.125[/tex]
In the case that the chance of having a boy is p'=0.51, the probabiltity of having 3 boys become:
[tex]P(X=BBB)=p'^3=0.51^3=0.133[/tex]
The radius of a certain wheel is 7 inches. Which of the following is closet to the circumference of the wheel?
A. 10.99,
B. 21.98,
C. 14.21,
D. 43.96
100 POINTS
PLEASE EXPLAIN AND ADD STEPS. THANK YOU IN ADVANCE
Given one to one f(6)=3, f'(6)=5, find tangent line to y=f⁻¹(x) at (3,6)
OK, we know
f⁻¹(3)=6
The inverse function is the reflection in y=x. So slopes, i.e. the derivative will be the reciprocal. We know the derivative of f at 6 is 5, so the derivative of f⁻¹ at y=6 is 1/5, which corresponds to x=3.
f⁻¹ ' (3) = 1/5
That slope through (3,6) is the tangent line we seek:
y - 6 = (1/5) (x-3)
That's the tangent line.
y = x/5 + 27/5
First, find the inverse function.
Note that an inverse is a reflection; y = x
The derivative given will be the reciprocal and when f is at 6, it equals 5. So, when it is at y = 6 it is at x = 1/5 and corresponds to 3.
f^-1(3) = 1/5
The point (3, 6) is the point in which the slope goes through. We can write all this information in slope-intercept form.
y = 1/5x + 27/5
Best of Luck1
Write and equation in slope intercept form for the line with the slope 3/5 and y intercept -3
Answer:
y = 3/5x + (-3)
Step-by-step explanation:
because slope intercept form is y = mx + b
and m = 3/5
and b = -3
so you plug them in to the formula and there's your answer
The equation in slope-intercept form for the line with a slope of 3/5 and a y-intercept of -3 is y = (3/5)x - 3.
We have,
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Slope (m) = 3/5
Y-intercept (b) = -3
Plug in the values of the slope and y-intercept into the equation.
y = (3/5)x - 3
Therefore,
The equation in slope-intercept form for the line with a slope of 3/5 and a y-intercept of -3 is y = (3/5)x - 3.
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There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In the second game you win if you can throw more than 80 % heads. For each game would you rather flip the coin 30 times or 300 times?
a) 300 times for each game
b. 30 times for each game
c) ç30 times for the first game and 300 times for the second
"d) 300 times for the first game and 30 times for the second
Answer:
d) 300 times for the first game and 30 times for the second
Step-by-step explanation:
We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.
As the coin is flipped more than one time and calculated the proportion, we have to use the sampling distribution of the sampling proportions.
The mean and standard deviation of this sampling distribution is:
[tex]\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}[/tex]
We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.
The probability of getting a proportion within this interval can be calculated as:
[tex]P(0.45<x<0.55)=P(z_L<z<z_H)[/tex]
referring the z values to the z-score of the standard normal distirbution.
We can calculate this values of z as:
[tex]z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)<0[/tex]
If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.
With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.
For the second game, we win if we get a proportion over 80%.
The probability of winning is:
[tex]P(p>0.8)=P(z>z^*)[/tex]
The z value is calculated as before:
[tex]z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0[/tex]
As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).
If our chances of winnings depend on P(z>z*), they become lower as z* increases.
Then, we can conclude that our chances of winning decrease with the increase of the number of trials.
We prefer the option of 30 trials for this game.
Final answer:
For the first game where 45% to 55% heads are needed, flipping the coin 300 times is beneficial due to the law of large numbers. For the second game requiring over 80% heads, flipping only 30 times is better to have a higher chance of deviation from the theoretical probability. So the correct option is d.
Explanation:
In determining whether you would rather flip a coin 30 times or 300 times for each game, one must consider the law of large numbers, which implies that as the number of trials increases, the experimental probabilities tend to get closer to the theoretical probabilities. In this case, a fair coin has a 50% chance of landing on heads on any given flip.
For the first game, where you win if you land between 45% and 55% heads, it's advantageous to flip the coin more times. This is because, with a larger number of flips (like 300), the results are more likely to converge to the expected probability, making it more probable you'll land within that range. Hence, you should choose 300 flips for the first game.
For the second game, where you win if you land more than 80% heads, you would prefer fewer flips, such as 30. It's less likely for a fair coin to consistently land on heads as the number of flips increases, so reducing the number of flips increases the chance of a more significant deviation from the expected probability.
The correct answer, therefore, would be option d: 300 times for the first game and 30 times for the second game.
match the numbers with the correct label. i will MARK YOU BRAINLIEST if your right, only answer if you know what your doing!!! :))
Answer:
a = 1/7, b = 0.2, c = 3/9
Step-by-step explanation:
[tex]0.2=\frac{2}{10} = \frac{1}{5}[/tex]
[tex]\frac{1}{7}[/tex]
[tex]\frac{3}{9}=\frac{1}{3}[/tex]
[tex]\frac{1}{5} > \frac{1}{7}[/tex] placing it farther along the number line, making 0.2 the red label (b)
[tex]\frac{1}{7}[/tex] is the smallest fraction that you are given, so it will be closest to 0, making it the blue label (a)
[tex]\frac{1}{3} > \frac{1}{4}[/tex] so [tex]\frac{3}{9}[/tex] is the green label (c)
The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1400 hours and a standard deviation of 55 hours. Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?
Answer:
By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 1400 hours
Standard deviation = 55 hours
Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?
1345 = 1400 - 1*55
So 1345 is one standard deviation below the mean.
1455 = 1400 + 1*55
So 1455 is one standard deviation above the mean.
By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours