Select the correct statement about what data scientists do during the Data Preparation stage.
a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.
Answer:
e. All of the above statements are correct.
Option e is correct. All of the above statements are correct.
What is Data science?Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data
Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.
During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.
Hence, All of the above statements are correct, Option e is correct.
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A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.
Answer:
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Step-by-step explanation:
Before testing the hypothesis, 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
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.
California:
Sample of 296 voters, 146 voted. This means that:
[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]
[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]
Colorado:
Sample of 215 voters, 127 voted. This means that:
[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]
[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]
Test if the population proportion of voter turnout in Colorado is higher than that in California:
At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So
[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]
At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So
[tex]H_1: p_{Co} - p_{Ca} > 0[/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]
From the two samples:
[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 = 0.0975[/tex]
[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]
[tex]z = 2.2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.
Looking at the z-table, z = 2.2 has a p-value of 0.9861.
1 - 0.9861 = 0.0139.
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Bill works for a large food service company. In one hour he can make 19 sandwiches or he can make 40 salads. Bill works 7 hours per day. If Bill needs to make 30 sandwiches then how many salads can he make
Answer:
[tex]x=216 salads[/tex]
Step-by-step explanation:
One Hour:
Salad=40
Sandwich=19
Total work time[tex]T=7[/tex]
Generally
Time to make 30 sandwiches is
[tex]T_s=\frac{30}{19}[/tex]
[tex]T-s=1.6hours[/tex]
Therefore
Bill has 7-1.6 hours to make salads and can make x about of salads in
[tex]x=(7-1.6)*40[/tex]
[tex]x=5.4*40[/tex]
[tex]x=216 salads[/tex]
Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)
Answer:
(in attachment)
Step-by-step explanation:
you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.
When x=-4
y=1/2(-4)
y=-2
(-4,-2)
Repeat for all values.
Which of the following tables represent valid functions?
Answer:
Step-by-step explanation:
A relation may or may not represent a function.
Table (a), (c) and (d) represent a function
The tables represent a relation
For a relation to be a function, then:
The y values must have unique (or distinct) x-values.
From the list of tables, we have the following observations
All y values in table (a), have different corresponding x valuesy values 3 and 6 in table (b), point to the same x value (2)All y values in table (c), have different corresponding x valuesAll y values in table (d), have different corresponding x valuesHence, all the tables represent a valid function, except table (b)
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i’ll make brainliest
look at the photo and check my work?
also tell me the answer to the ones i didn’t do
thanks :)
Which of these are related functions. Plato
Answer:
◦•●◉these are related functions
Consider points a, b, and c in the graph. Determine which of these points is relative minima on the interval x = –1 and x = –2 in the graph.
Answer:
C.
Step-by-step explanation:
1) note, the point "а" belongs to the given interval only, then
2) the correct answer is C) a.
Answer:
as we can see here point {\color{Red}a} lies on the interval (-2, -1)
so option A is correct
Step-by-step explanation:
Suki makes and sells denim jackets in a small store at the mall. She has found that
the following system of equations represents the expenses and the revenue for
running her store.
C = 520 + 31n
C = 96n
Determine the minimum number of jackets she must sell to make a profit.
Answer:
8
Step-by-step explanation:
96n = 520 + 31n
65n=520
n=8
Hope this helps :)
g From a distribution with mean 38 and variance 52, a sample of size 16 is taken. Let X be the mean of the sample. Show that the probability is at least 0.87 that X is in (33, 43)
Answer:
[tex]P=8.869[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =38[/tex]
Variance [tex]\sigma=52[/tex]
Sample size [tex]n=16[/tex]
[tex]X=(33, 43)[/tex]
Generally the equation for Chebyshev's Rule is mathematically given by
[tex]A=(1-\frac{1}{k^2})*100\%[/tex]
Where
[tex]k=\frac{\=x-\mu}{\frac{\sigma}{\sqrt n}}}}[/tex]
[tex]k=\frac{43-38}{\frac{52}{\sqrt 16}}}}[/tex]
[tex]k=2.77[/tex]
Therefore
Probability
[tex]P=(1-\frac{1}{2.77^2})[/tex]
[tex]P=8.869[/tex]
Given a set of data that is skewed-left, there is at least _____ % of the data within 2 standard deviations.
Answer:
75
Step-by-step explanation:
For non-normal distributions, we use Chebyshev's Theorem.
Chebyshev Theorem
The Chebyshev Theorem states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Within 2 standard deviations of the mean, so 75%.
A teacher calculates for the test grades in
Class A, mean = 32 and sd = 4
Class B, mean = 32 and sd = 8
a. If the teacher was going to guess what any student in his/her class would earn, what is the best score
to guess?
b. Which of the classes has more consistency in their scores? Why?
Answer:
a. best score to guess would be 33
b. Standard deviation simplifies the square root of the mean so makes it closer to 1 has more consistency as the mean of 32 when squared is sqrt 32 is Class A as class a = 4 and is closer to 5.65685425
as 5.65685425^2 = 32
Step-by-step explanation:
If you are comparing two normally-distributed variables on the same measurement scale then yes, you can regard the standard deviation as an indicator of how reliable the mean is--the smaller the standard deviation, the better able you are to "zero in" on the actual population mean.
a. proofs;
We find 32/6 = 5.333 and 32/5 = 6.4 and 6.4 is closer to both sd 4 and 8 than 5.33 is. As 6.4 it is closer to 6
But when we use 33/6 = 5.5 and therefore shows close range 6
therefore the two sd proves it is slightly high 32 score average for both classes A + B when joined and high 32 = 33 mean when classes A+B are joined or you could say 32/8 = 4 is class B becomes lower tests scores as 32/4 = 8 of class A that has higher test scores.
In this exercise we have to use probability and statistics to organize the students' grades, so we have:
A) best score is 33
B) Class A
In the first part of the exercise we have to analyze the grades of each class, like this:
A)Class A: 32/4
Class B: 32/8
Dividing each of them we have:
[tex]32/4=8 \\32/8=4[/tex]
B) With the information given above, we can say that the best class is A.
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Solve For X any and all help is appreciated (:
Answer:
x is 3
Step-by-step explanation:
You use proportions to figure out x, what you first do is set up the proportion of the big triangle, then the small triangle.
[tex]\frac{(9+3)}{3}[/tex]= [tex]\frac{12}{x}[/tex]
By setting up this proportion, you would then cross multiply, and get 12x = 36. This is when you divide by 12 on both sides and get x=3
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
See this attachment
[tex]\boxed{\boxed{\sf{ x=3 }}}[/tex] [tex]\sf{ }[/tex]
Solve for x:
|3x-1|=4
Answer:
x = 5/3 x= -1
Step-by-step explanation:
|3x-1|=4
There are two solutions to the absolute value equation, one positive and one negative
3x-1 =4 and 3x-1=-4
Add 1 to each side
3x-1+1 = 4+1 3x-1+1 = -4+1
3x=5 3x = -3
Divide by 3
3x/3 = 5/3 3x/3 = -3/3
x = 5/3 x= -1
A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filling a cup between 33 and 35 ounces? Round your answer to four decimal places.
Answer:
0.8919 = 89.19% probability of filling a cup between 33 and 35 ounces.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces.
This means that [tex]\mu = 29, \sigma = 4[/tex]
What is the probability of filling a cup between 33 and 35 ounces?
This is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 33.
X = 35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 29}{4}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 33
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 29}{4}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.0413.
0.9332 - 0.0413 = 0.8919
0.8919 = 89.19% probability of filling a cup between 33 and 35 ounces.
Answer:
0.1598
Step-by-step explanation:
I need help with this
Answer:
Yes because 5^2 + 12^2 = 13^2
Step-by-step explanation:
We can check using the Pythagorean theorem
a^2 + b^2 = c^2
5^2 + 12^2 = 13^2
25+ 144= 169
169 = 169
9514 1404 393
Answer:
D. Yes, because 5² +12² = 13²
Step-by-step explanation:
To determine if a triple of three numbers will form a right triangle, see if they satisfy the Pythagorean theorem. If they do, the sum of the squares of the smaller two numbers will equal the square of the largest.
Here, we have ...
5² + 12² ?? 13²
25 +144 ?? 169
169 = 169 . . . . . . these side lengths will form a right triangle
_____
Additional comment
Three integer numbers like these that will satisfy the Pythagorean theorem are called a "Pythagorean triple." A few such triples that are commonly seen in algebra and trig problems are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)
It is worthwhile to remember a few of these, as you will see them again.
et f(x)=6(2)x−1+4. The graph of f(x) is translated 7 units to the left to form the graph of g(x). Enter the equation for g(x) in the box.
Answer:
[tex]g(x) = 6(2)^{x -8}+ 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6(2)^{x - 1}+ 4[/tex]
Required
Find g(x)
From the question, f(x) is translated 7 units left;
The rule of translation is: [tex](x,y) \to (x-7,y)[/tex]
So, we have:
[tex]g(x) = f(x - 7)[/tex]
[tex]g(x) = 6(2)^{x -7- 1}+ 4[/tex]
[tex]g(x) = 6(2)^{x -8}+ 4[/tex]
Which of the following is an arithmetic sequence?
O 1,-3,9,-27...
0-2, 4, -6, 8, ...
-8, -6, -4,-2....
O2, 4, 8, 16, ...
9514 1404 393
Answer:
(c) -8, -6, -4, -2, ...
Step-by-step explanation:
An arithmetic sequence has sequential terms that have a common difference.
The first differences of the offered sequences are ...
a) -4, 12, -36
b) 6, -10, 14
c) 2, 2, 2 . . . . . . constant, so an arithmetic sequence
d) 2, 4, 8
__
The arithmetic sequence is -8, -6, -4, -2, ....
An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.
Answer: See explanation
Step-by-step explanation:
1. Use the five steps of hypothesis testing.
Step 1: The aim of the research is to conduct the five steps of hypothesis testing.
Step 2:
Null hypothesis: H0 u= 4
Population mean: H1 u = 4
Alternate hypothesis: u ≠ 4
Population mean: u ≠ 4
Step 3 and step 4 are attached.
Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.
2. Sketch the distributions involved
This has been attached.
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.
The distribution is "t".
The means is tested by using T-test.
Chi-square is used to test the single variance.
Write an equation of the line that passes through a pair of points: (-5, -2), (3, -1) y=-x+ C. y=-- x - 11 11 a. 8 8 b. 11 d. y=-x+ 8 y=-x - 8 11
Answer:
y = 8x+11
Step-by-step explanation:
The coordination of the points are : (-5,-2) , (3, -1)
Then, the equation is :
[tex]\frac{y+5}{x+2} =\frac{-5-3}{-2+1} \\\\or,\frac{y+5}{x+2} = 8\\or, y+5=8(x+2)\\or, y = 8x+16-5\\y= 8x+11[/tex]
Point A lies outside of plane P, how many lines can be drawn parallel to plane P that pass through point A?
A. 0
B. 1
C. 2
D. an infinite number
Answer:
B. an infinite number
Step-by-step explanation:
Since point A lies outside of P, the number of lines that can be drawn parallel to P and passing through point A is only infinite. It is infinite because it is just one given point lying outside the plane. If there is more than one point then it will be otherwise.
Answer:
yeah
Step-by-step explanation:
In this graph, which transformation can produce quadrilateral A′B′C′D′ from quadrilateral ABCD?
Answer:
A reflection across the y axis and then a reflection across the x axis
Step-by-step explanation:
Answer:
An 180 degree counterclockwise rotation around the origin
Step-by-step explanation:
plato/edmuntum answer
g Let the joint probability density function of random variables X and Y. (a) Calculate the marginal probability densities of X and Y . (b) Calculate the expected values of X and Y . be given by
Answer: hello your question is incomplete attached below is the complete question
answer:
a) Fx(X) = 0 ≤ x ≤ 2, Fy(Y) = y - y^3/4
b) E(X) = 32/20 , E(Y) = 64/60
Step-by-step explanation:
a) Marginal probability density
Fx(X) = [tex]\int\limits^x_0 {\frac{xy}{2} } \, dy[/tex]
∴ probability density of X = 0 ≤ x ≤ 2
Fy(Y) = [tex]\int\limits^2_y {\frac{xy}{2} } \, dx[/tex]
∴ probability density of Y = y - y^3/4
b) Determine the expected values of X and Y
E(X) = 32/20
E(Y) = 64 /60
attached below is the detailed solution
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 440 grams with a variance of 441. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.
Answer:
The null hypothesis is [tex]H_0: \mu = 444[/tex]
The alternative hypothesis is [tex]H_1: \mu < 444[/tex]
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.
At the null hypothesis, we test if the machine works correctly, that is, the mean is of 444. So
[tex]H_0: \mu = 444[/tex]
At the alternative hypothesis, we test if they are underfilling, that is, if the mean is of less than 444. So
[tex]H_1: \mu < 444[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
444 is tested at the null hypothesis:
This means that [tex]\mu = 444[/tex]
A 41 bag sample had a mean of 440 grams with a variance of 441.
This means that [tex]n = 41, X = 440, s = \sqrt{441} = 21[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{440 - 444}{\frac{21}{\sqrt{41}}}[/tex]
[tex]t = -1.22[/tex]
P-value of the test:
Right-tailed test(test if the mean is less than a value), with 41 - 1 = 40 df and t = -1.22.
Using a t-distribution calculator, this p-value is of 0.1148
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on tails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game
Answer:
On average, a player should expect to win $15.
Step-by-step explanation:
The expected value in an event with outcomes:
x₁, x₂, ..., xₙ
Each with probability:
p₁, ..., pₙ
is given by:
Ev = x₁*p₁ + ... +xₙ*pₙ
In this case we have 3 outcomes:
player wins $75 = x₁
player wins $45 = x₂
player does not win = x₃
Let's find the probabilities of these events.
player wins $75)
Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75
While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)
Then the number total of outcomes is:
C = 2*2*2 = 8
Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)
p₁ = 1/8
Win $45:
This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:
p₂ = 1/8
Not wining:
Remember that:
p₁ + p₂ + ... + pₙ = 1
Then for this case, we must have:
p₁ + p₂ + p₃ = 1
1/8 + 1/8 + p₃ = 1
p₃ = 1 - 1/8 - 1/8
p₃ = 6/8
Then the expected value will be:
Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15
On average, a player should expect to win $15.
add:7ab,8ab,-10ab,-3ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+(-10ab)+(-3ab)=
=15ab-13ab= 2ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+-10ab+-3ab
Factor out ab
ab(7+8-10-3)
ab(2)
2ab
Whats The Correct Answer?!
Answer: the correct answer is D 0.05
Step-by-step explanation:
Answer:
0.02 m/s
Step-by-step explanation:
42/50 meters in 26/30 minutes,
26/30 minutes = 52 seconds
so in 1 second, 42/50 ÷ 52
= 42/50 × 1/52
= 21/1300
= 0.02 (approximately)
Answered by GAUTHMATH
A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000. To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245. Can you conclude that the mean monthly rent in the city is less than $1000
Answer:
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
Step-by-step explanation:
A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000.
At the null hypothesis, we test if the mean is of at least $1000, that is:
[tex]H_0: \mu \geq 1000[/tex]
At the alternative hypothesis, we test if the mean is less than $1000, that is:
[tex]H_1: \mu < 1000[/tex]
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
1000 is tested at the null hypothesis:
This means that [tex]\mu = 1000[/tex]
To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245.
This means that [tex]n = 47, X = 941, s = 245[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{941 - 1000}{\frac{245}{\sqrt{47}}}[/tex]
[tex]t = -1.65[/tex]
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with t = -1.65 and 47 - 1 = 46 df.
Using a t-distribution calculator, the p-value is of 0.053.
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest.
b. The probability of winning a lottery is 0.125, what is the probability of winning at least once in twelve trials?
Part (a)
If you win $12165, then you really net 12165-35 = 12130 dollars when you consider the ticket fee. So this is the true amount of money you win, or take home at the end of the day. This is before taxes.
Multiply 0.002 with 12,130 to get 0.002*12130 = 24.26
We'll use this later so let A = 24.26
The chances that you don't win are 1 - 0.002 = 0.998 which multiplies with -35 to indicate you lost $35 in playing the game. So we get B = 0.998*(-35) = -34.93
Lastly, add the values of A and B to get the expected value:
A+B = 24.26 + (-34.93) = -10.67 is the expected value.
On average, you expect to lose about $10.67 for any time you play the game.
Answer: -10.67 dollars===========================================================
Part (b)
0.125 is the probability of winning so 1-0.125 = 0.875 is the probability of losing.
Let's say you get really unlucky and lose 12 times in a row. Assuming each trial (aka case when you play the game) is independent, this would mean the probability of such an event is (0.875)^12 = 0.2014172, which is approximate.
Subtract that from 1 to get the probability of winning at least once
1 - (0.875)^12 = 1 - 0.2014172 = 0.7985828
which is also approximate. If we rounded to three decimal places, then it would be 0.799; I'm picking three decimals since 0.125 is to three decimal places. Round however you need to if otherwise.
Answer: 0.799 (approximate)A, B, and C are points of tangency. CQ = 5, PQ = 10, and PR = 14. What is the perimeter
of the triangle PQR?
*see attachment for diagram
Answer:
Perimeter = 38
Step-by-step explanation:
Recall: when two tangents are drawn to meet at a point outside a circle, the segments of the two tangents are congruent.
Given,
CQ = 5
PQ = 10
PR = 14
Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
CQ = QB = 5 (tangents drawn from an external point)
BP = PQ - QB
BP = 10 - 5 = 5
BP = PA = 5 (tangents drawn from an external point)
AR = PR - PA
AR = 14 - 5 = 9
AR = RC = 9 (tangents drawn from an external point)
✔️Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
= 9 + 5 + 5 + 5 + 5 + 9
Perimeter = 38
