Answer:
The value of the test statistic is [tex]z = 1.78[/tex]
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 110, s_1 = \frac{7.2}{\sqrt{81}} = 0.8[/tex]
Sample 2:
[tex]\mu_2 = 108, s_2 = \frac{6.3}{\sqrt{64}} = 0.7875[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
Distribution of the difference:
[tex]X = \mu_1 - \mu_2 = 110 - 108 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.8^2+0.7875^2} = 1.1226[/tex]
What is the value of the test statistic?
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{2 - 0}{1.1226}[/tex]
[tex]z = 1.78[/tex]
The value of the test statistic is [tex]z = 1.78[/tex]
At a festival you run across a booth with an interesting game. Tokens are sold for $2 with a selection of prizes. There is a $25 grand prize which you have a 5% chance of winning, there are 5 mid-level prizes, each worth $15 with a 15% chance of winning, and there is a consolation prize worth $1 with a 20% chance of winning. What is your expected gain or loss if you play this game
Answer:
Your expected gain is of $10.7.
Step-by-step explanation:
Expected earnings:
The expected earnings is each prize multiplied by it's probability of being earned.
So
5% probability of earning $25.
5*15% = 75% probability of earning $15.
20% probability of earning $1. So
0.05*25 + 0.75*15 + 0.2*1 = 12.7
Cost of token:
The token costs $2, which means that we subtract $2 from the expected earnings.
12.7 - 2 = 10.7
Your expected gain is of $10.7.
Can someone check those and tell what is wrong and the answer
Answer:
42. acute
43. obtuse
Step-by-step explanation:
Obtuse: which one of the interior angles measures more than 90° degrees, then the rest are less than ninety.
Acute: all less than ninety and all different.
The line passes through points (2,7) and (4,8)
Answer:
Explanation:
hope it will helps please heart my answer!
when accessing your credit card ,information online you cannot
Answer:
C. make purchases
Step-by-step explanation:
took the test
Equation: -5 3/4- 3 1/2 Please help meh.
Answer:
[tex]-9\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]-5\frac{3}{4}-3\frac{1}{2}[/tex]
Step 1: Factor out the common term [tex]-1[/tex]
[tex]=-\left(5\frac{3}{4}+3\frac{1}{2}\right)[/tex]
Step 2: Add the whole numbers
[tex]5 + 3 = 8[/tex]
Step 3: Combine the fractions:
[tex]\frac{3}{4}+\frac{1}{2} = \frac{5}{4}\\\\=-\left(8+\frac{5}{4}\right)[/tex]
Step 4: Convert the improper fractions to mixed numbers
[tex]\frac{5}{4} = 1\frac{1}{4}\\\\=-\left(8+1\frac{1}{4}\right)[/tex]
Step 5: Add the numbers
[tex]8 + 1 =9 \\\\=-9\frac{1}{4}[/tex]
Therefore, the answer to the equation is [tex]-9\frac{1}{4}[/tex] in fraction, and decimal; [tex]9.25[/tex]
Find the probability of at least one
failure in five trials of a binomial
experiment in which the probability of
success is 30%.
Round to the nearest tenth of a
percent.
Answer:
99.8% probability of at least one failure.
Step-by-step explanation:
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.
Probability of success is 30%.
This means that [tex]p = 0.3[/tex]
Five trials:
This means that [tex]n = 5[/tex]
Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%.
Less than five sucesses, which is:
[tex]P(X < 5) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.002[/tex]
[tex]P(X < 5) = 1 - P(X = 5) = 1 - 0.002 = 0.998[/tex]
0.998*100% = 99.8%
99.8% probability of at least one failure.
Help me please I need to get a good grade on this
Answer: 1,000
Step-by-step explanation: if you multiply the 900 in 157,900 by a 1,000 you get the 900,000 in 901,532.
How can you check the sample space of a probability model?
Answer: The sample space S for a probability model is the set of all possible outcomes. For example, suppose there are 5 marbles in a bowl. One is red, one is blue, one is yellow, one is green, and one is purple.
Step-by-step explanation: Hope this helped :)
Write the phrase as a numerical or algebraic expression: 7 more than 16n
Answer:
16n + 7
Step-by-step explanation:
Answer:
7 + 16n
Step-by-step explanation:
The use of more than indicates addition.
The heights of seasonal pine saplings are normally distributed with an unknown population mean and standard deviation. A random sample of 20 saplings is taken and results in a sample mean of 310 millimeters and sample standard deviation of 20 millimeters. (a) The EBM, margin of error, for a 98% confidence interval estimate for the population mean using the Student's t-distribution is 11.35. (b) Find a 98% confidence interval estimate for the population mean using the Student's t-distribution. Round the final answers to two decimal places.
Answer:
a) The margin of error for the interval is of 11.35.
b) The 98% confidence interval estimate for the population mean using the Student's t-distribution is between 298.65 and 321.35 millimeters.
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 = 20 - 1 = 19
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.539
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.539\frac{20}{\sqrt{20}} = 11.35[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Thus, the margin of error for the interval is of 11.35.
The lower end of the interval is the sample mean subtracted by M. So it is 310 - 11.35 = 298.65 millimeters.
The upper end of the interval is the sample mean added to M. So it is 310 + 11.35 = 321.35 millimeters.
The 98% confidence interval estimate for the population mean using the Student's t-distribution is between 298.65 and 321.35 millimeters.
What is 5x(4+3.50+6+2.50)
Answer: the answer is 80
Step-by-step explanation: How i got this answer is i followed the PEMDAS order (parenthesis, exponent, multiplication, division, addition, subtraction)
So according to the order, i had to do the parenthesis first, (4+3.50+6+2.50)
(( what i did was i just broke the problems into 2 so it would be much more easier)) (4 + 3.50 = 7.5) and the next (6 + 2.50 = 8.5) Then you would add those numbers together (7.5 + 8.5 = 16)
We can see that we still have the 5 left over, so now all you gotta do is just multiply now. (16 x 5 = 80)
So the answer u r left off with is 80.
~hope this has helped you out, have a gr8 day/night my friend!~
In a certain Algebra 2 class of 30 students, 14 of them play basketball and 10 of them play baseball. There are 14 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Help a man out
PLZ HELP NEEDED ASAP WILL GIVE BRAINLIEST
Answer:
32
Step-by-step explanation:
freedom and creative expression
The number 32 symbolizes freedom and creative expression. It is also a number that symbolizes teamwork, relationships, sensuality, optimism, curiosity. Number 32 people are tolerant, adventurous. and witty. They have a need to be spontaneous and free. They are interested in many things.
ben is tiling the floor in his bathroom. the area he is tiling is 4m x 2m. each tile is 400m x 400 mm. he has 45 tiles. is this enough
If the line that connects the boat to the parasail is reeled in by 20
meters and the angle of elevation changes to 38° from the boat, how
many meters above the lake is the man to the nearest tenth of a
meter?
A)
67.4 m
B)
85.6 m
9
86.3 m
D)
177.9 m
Answer:
A) 67.4 m
Step-by-step explanation:
Let "x" represent how many meters above the lake is the man
Reference angle = 32°
Opposite = x
Hypotenuse = 129.5 m
Apply ye trigonometric function SOH:
Sin 32° = Opp/Hyp
Son 32 = x/129.5
129.5 × sin 32° = x
x = 68.6245447
This is close to A) 67.4 m
-11 2/3 x (-4 1/5) =
Answer:
49 is your answer :)
Step-by-step explanation:
Have a nice dayyy <3
100 points will mark brainliest
A randomized study compared two drugs that are designed to lower a person's triglyceride level. It was found that over a 1-year period, those receiving Drug A decreased their triglyceride level by a mean of 69. Those receiving Drug B decreased their triglyceride level by a mean of 45.
To determine whether the results are significant, the data are rerandomized and the difference of the means is shown in the dot plot.
What is the best conclusion to make based on the data?
a. The difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance.
b. The difference of the means is not significant because the rerandomizations show that it is within the range of what likely happens by chance.
c. The difference of the means is not significant because the rerandomizations show that it is outside the range of what likely happens by chance.
d. The difference of the means is significant because the rerandomizations show that it is outside the range of what likely happens by chance.
Answer:
a
Step-by-step explanation:
The difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance.
Option (A) difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance is the correct option.
What is a dot plot?"A dot plot is used to represent any data in the form of dots or small circles. It is similar to a simplified histogram or a bar graph as the height of the bar formed with dots represents the numerical value of each variable. Dot plots are used to represent small amounts of data".
For the given situation,
A randomized study shows the comparison of two drugs that are designed to lower a person's triglyceride level.
Drug A decreased their triglyceride level by a mean of 69.
Drug B decreased their triglyceride level by a mean of 45.
Mean difference = [tex]69-45[/tex]
⇒ Mean difference = [tex]24[/tex]
The data are rerandomized and the difference in the means is shown in the dot plot.
In the dot plot, the difference in the means is rerandomized and is arranged between the range 6 to 22.
Hence we can conclude that option (A) difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance is the correct option.
Learn more about the dot plot here
https://brainly.com/question/23498615
#SPJ2
I need help question attached. 20 point!
Answer:
[tex]45\:\mathrm{in}[/tex]
Step-by-step explanation:
The volume of a square pyramid is given by [tex]V=\frac{1}{3}\cdot s^2\cdot h[/tex]. Substituting given values, we have:
[tex]3,840=\frac{1}{3}\cdot 16^2\cdot h,\\h=\frac{3,840\cdot 3}{256}=\boxed{45}[/tex]
Answer:
30 in.
Step-by-step explanation:
[tex]h=3\frac{V}{a^{2} }[/tex]
[tex]h=3\frac{3840}{16^{2} }[/tex]
45.12
That is not an option, so go with the closest one 30 in.
The question is ...(see the picture)
Thank you very much！！
Answer: [tex]3x^{-2.5}[/tex]
Step-by-step explanation:
Given
Expression is
[tex]\dfrac{12\sqrt{x}}{4x^3}[/tex]
Using exponent property [tex]x^a\cdot x^b=x^{a+b}[/tex]
Writing expression in the form of [tex]k\cdot x^n[/tex]
[tex]\Rightarrow \dfrac{12\sqrt{x}}{4x^3}=\dfrac{3\times 4}{4}\times \dfrac{x^{0.5}}{x^3}\\\\\Rightarrow \dfrac{3\times 4}{4}\times x^{0.5-3}\\\\\Rightarrow 3x^{-2.5}[/tex]
A lottery game has balls numbered 1 through 15. What is the probability of selecting an even numbered ball or a 13?
Answer:
8 / 15
Step-by-step explanation:
Sample space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Required outcome :
Even numbers = (2, 4, 6, 8, 10, 12, 14) or 13
Total required outcomes = 8
Probability = required outcome / Total possible outcomes
P(even number or 13) = 8 / 15
Which of the following relation is a function.
Answer:
Which of the following relations is a function- A
Determine which relation is a function- A
Step-by-step explanation:
A function is a type of relationship where x's do not repeat. So, to solve find where each y has a unique x value. In the first question, A is correct because the x values; -3, 0, 2; never repeat. Then, on the next question A is correct because it is a relation written in slope-intercept form, which is a type of function notation.
You want to measure the height of a tree in
front of your house. You are standing 25
feet away from the tree, and you are
looking at the top of the tree with an angle
of elevation of 52º. What is the height of
the tree? Round to the nearest foot.
Answer:
31 feets
Step-by-step explanation:
The sketched triangle of the problem is attached below :
To byian the height h of the tree :
We use the trigonometric relation :
Tan θ = opposite / Adjacent
Tan 52 = h / 25
1.2799416 = h / 25
h = 1.2799416 * 25
h = 31.998540
h = 32 feets
Evaluate cos0 if sin0= sqrt(5)/3
a. 9/5
b. 2/3
c. 5/9
d. 3/2
Solution given:
[tex] \sin( \alpha ) = \frac{\sqrt{5} }{3}[/tex]
so
P=√5
h=3
b=[tex] \sqrt{3 {}^{2} - \sqrt{5} {}^{2} } [/tex]
b=2
so
[tex] \cos( \alpha ) = \frac{b}{h} = \frac{2}{3} [/tex]
Note
[tex] \alpha = 0[/tex]
b:⅔
Perpendicular=√5
Hypotenuse=3
Base
√(3)²-(√5)²√9-5√42CosØ
Base/Hypotenuse2/3Please somebody help me out!!
Answer:
See below.
Step-by-step explanation:
These work just like ordinary algebraic expresssions, except you have to remember always: i^2 = -1 i squared is negative one!
(4 - 3i)(4 + 3i) "FOIL" the expression to get 16 - 3i + 3i - 9i^2. But i^2 = -1, so this is the same as 16 - 3i + 3i + 9. Combine like terms.
Ans. 25
(4 - 3i)(i) Distribute the i to the two terms of the binomial.
4i - 3i^2 = 4i - 3(-1)
Ans. 4i + 3
(6i)(4 + 3i) = (6i)(4) + (6i)(3i) = 24i + 18i^2 = 24i + 18(-1)
Ans. 24i -18
(6i)(i) = 6i^2 = 6(-1)
Ans. -6
(-5)(4 + 3i) = -20 - 15i That's it; there's no i^2 to deal with.
Ans. -20 - 15i
(-5)(i) = -5i Again, that's all there is to it.
Ans. -5i
transformati in unitati principale de masura pentru:
lungime
I upped the steaks plz answer this, I will give brainiest
Answer:
[tex] \displaystyle x = \frac{3}{4} [/tex]
Step-by-step explanation:
we are given that
[tex] \displaystyle P = \left(x, - \frac{ \sqrt{7} }{4} \right)[/tex]
we want to figure out x
remember that,
In unit circle x coordinate is considered cos and y coordinate is considered sin
so in order to figure out x we should figure out the value of cos to do we can consider Pythagoras trig indentity
given by
[tex] \displaystyle \sin ^{2} ( \theta) + { \cos}^{2} ( \theta) = 1[/tex]
we are given sin=-√7/4 thus
substitute:
[tex] \displaystyle \left( - \frac{ \sqrt{7} }{4} \right) ^{2} + { \cos}^{2} ( \theta) = 1[/tex]
simplify square:
[tex] \displaystyle \frac{7}{16} + \cos ^{2} ( \theta) = 1[/tex]
move left hand side expression to right hand side and change its sign:
[tex] \displaystyle \cos ^{2} ( \theta) = 1 - \frac{7}{16} [/tex]
simplify Substraction:
[tex] \displaystyle \cos ^{2} ( \theta) = \frac{9}{16} [/tex]
square root both sides:
[tex] \displaystyle \cos ^{} ( \theta) = \pm\frac{3}{4} [/tex]
since in unit circle cos is x and P belongs to Q:IV negative cos isn't applicable
hence,
[tex] \displaystyle x = \frac{3}{4}[/tex]
Miley walks dogs to earn money. She tracks her steps while she walks the dogs so she can walk them all an equal distance. Last week, she walked 11 11 dogs. Her total distance was 4 , 532 4,532 yards. How far did she walk each dog?
Answer:
412 yards each
Step-by-step explanation:
4,532/11=412
A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 78 jobs and a standard deviation of 6. Where do we expect approximately 95% of the distribution to fall? between 90 and 96 jobs per day between 72 and 84 jobs per day between 60 and 96 jobs per day between 66 and 90 jobs per day
Answer:
The answer is "between 60 and 96 jobs per day".
Step-by-step explanation:
In this solution, there is a mound-sized and symmetrical distribution for the number of works submitted to your computer per day with mean=78, and standard deviation=6.
Therefore a distribution of 95% decreases between the average [tex]\pm[/tex] 3* standard deviation
Therefore,
[tex]\to 78\pm (3*6)=(78-18, 78+18)=(60,96)[/tex]
The 95% distribution falls in between 60 and 96 jobs per day.
2/3 a minus 1/6 equals 1/3 what is a
Answer:
a = 3/4.
Step-by-step explanation:
2a/3 - 1/6 = 1/3
Multiply thru by the LCD 6:
4a - 1 = 2
4a = 3
a = 3/4.
What is the 100th term of this sequence?
an= -7n+ -5