X and Y are both standard normal random variables (mean = 0, standard deviation = 1), statistically independent of each other. Using the DATA IN THE ATTACHED FILE, estimate the probability that X and Y are both positive and that their sum is less or equal to 1. This probability is
Answer:
The probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
Step-by-step explanation:
It is provided that the random variables X and Y follows a standard normal distribution.
That is, [tex]X,Y\sim N(0, 1)[/tex]
It is also provided that the variables X and Y are statistically independent of each other.
Compute the probability that X and Y are both positive and that their sum is less or equal to 1 as follows:
The mean and standard deviation of X + Y are:
[tex]E(X+Y)=E(X)+E(Y)=0+0=0\\\\SD(X+Y)=\sqrt{V(X)+V(Y)+2Cov(X,Y)}=\sqrt{1+1+0}=\sqrt{2}[/tex]
The probability is:
[tex]P(X+Y\leq 1)=P(X+Y<1-0.50)\ [\text{Apply continuity correction}]\\[/tex]
[tex]=P(X+Y<0.50)\\\\=P(\frac{(X+Y)-E(X+Y)}{SD(X+Y)}<\frac{0.50-0}{\sqrt{2}})\\\\=P(Z<0.354)\\\\=0.63683\\\\\approx 0.64[/tex]
*Use the z-table.
Thus, the probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
Please answer this correctly
Answer: 30
Step-by-step explanation:
Q1: 120
Q3: 150
To find the interquartile range, subtract Q1 from Q3, which is 150-120. Therefore, the interquartile range of the kitten's weight, is 30
Answer: 30 grams
Step-by-step explanation:
The interquartile range is the range within the boxed areaa. You subtract the minimum value from the maximum value.
150 - 120 = 30
Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.
Answer:
a) The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
We are 95% confident that the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is within 9,009 and 10,585 steps.
b) No, we can not use the confidence interval to estimate the probability of individual values. It can onlybe used to make inference about the population mean.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=9,797.
Ths sample standard deviation is s=2,313.
The sample size is N=61.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2313}{\sqrt{61}}=\dfrac{2313}{7.81}=296.15[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=61-1=60[/tex]
The t-value for a 99% confidence interval and 61 degrees of freedom is t=2.66.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.66 \cdot 296.15=787.84[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 9797-787.84=9009\\\\UL=M+t \cdot s_M = 9797+787.84=10585[/tex]
The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
b) The value of 8,500 steps is outside the confidence interval, but this means that it is an unusual value for the mean number of steps for all people in New York City who wear an activity tracker.
We can not use the confidence interval to estimate the probability of individual values.
The activity tracking devices.
The activity tracker re those devices such as watches and a bands that tells you about your physical activity such as skipping, running, and walking. They simply count the steps and tell you about the daily goals and targets. They are quite effective for monitoring blood pressure and more.
Thus answer is 9,009, 10,585 workers, 9,009, and 10,585 steps and population mean.
As per the question, the smart trackers are used by the new york people on a daily basis and they measure the footsteps of the people. A sample of random 61 people was taken and selected on the basis of the tracers. It was found that with these statistical tests a 99% confidence interval was taken for the mean on a typical workday for all people working in City that is 9,009, 10,585. The 95% confidence that the mean number of steps taken by workers of the City was within 9,009 and 10,585 steps.The confidence interval can be used to estimate the probability of the individual values. It can be used for drawing inferences for the population mean.Learn more about the trackers are electronic.
brainly.com/question/17434350.
"Two purple sea slugs are mated with each other. Among their numerous offspring, 428 have a purple integument and 152 have orange integuments. With a chi-square test, compare the observed numbers with a 3:1 ratio and determine if the difference between observed and expected could be a result of chance."
Answer:55
Step-by-step explanation:
55x1=55
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
PLEASE HELP
Answer: [tex]y=\frac{3}{2} x - 3[/tex]
Step-by-step explanation:
Looking at the graph we could locate the y intercept at point (0,-3) and we can locate another point (4,3) which also passes through the line. So using these coordinates we already know the the y-intercept as -3 but we need to find the slope to write it in slope intercept form.
To find the slope, we will need to find the difference in the y values and divide it by the difference in the x values.
(0,-3)
(4,3)
-3 - 3 = -6
0-4 = -4
-6 /-4 = 3/2 so now we know that the slope is 3 over 2
so we could write the equation as y = 3/2x -3
Answer: Thank you (nermay7)
Step-by-step explanation: They are correct!!!!!!!
A box is with a square base and open top is to be constructed and a total volume of 720 cubic inches is required. The cost of material for the base is 8 dollars per square inch and the cost of material for the sides is 6 dollars per square inch. Express the total cost of the box as a function of the length of the base.
Answer:
total cost = 8x^2 +17280/x
Step-by-step explanation:
Let x represent the base length. Then the area of the base is x^2, and the height is h = 720/x^2.
The area of the four sides is ...
(4x)(h) = (4x)(720/x^2) = 2880/x
The cost of the base is ...
base cost = 8x^2
And the cost of the sides is ...
side cost = 6(2880)/x = 17280/x
The total cost of the box is ...
total cost = base cost + side cost
total cost = 8x^2 +17280/x
_____
Comment on the cost function
You will find this function has a minimum at x=∛1080 ≈ 10.260 in. The total cost is about $2526.35, and the box is 2/3 times as tall as wide. That aspect ratio makes any pair of opposite sides cost the same as the base, the generic solution to a cost optimization problem of this sort.
Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational
Answer:
Step-by-step explanation:
5
A horizontal line contains points A, C, B. 2 lines extend from point C. A line extends to point E and another line extends to point D. An arc represents angle A C D.
Ray CE is the angle bisector of AngleACD. Which statement about the figure must be true?
mAngleECD = One-halfmAngleECB
mAngleACE = one-halfmAngleACD
AngleACE Is-congruent-to AngleDCB
AngleECDIs-congruent-to AngleACD
Answer:
Option (2).
Step-by-step explanation:
In the figure attached,
A, C and B are the points lying on a straight line.
2 lines EC and DC have been drawn by extending the lines from C to E and D respectively.
Ray CE is the angle bisector of ∠ACD.
That means CE divides ∠ACD in two equal parts.
m∠ACE = m∠DCE
Since m∠ACD = m∠ACE + m∠DCE
= 2(m∠ACE)
m∠ACE = [tex]\frac{1}{2}(\angle ACD)[/tex]
Therefore, option (2) will be the answer.
Answer:
b
Step-by-step explanation:
took test
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.18 and the probability that the flight will be delayed is 0.14. The probability that it
will not rain and the flight will leave on time is 0.74. What is the probability that the
flight would leave on time when it is not raining? Round your answer to the thousand
Answer:
0.902 = 90.2% probability that the flight would leave on time when it is not raining
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Not raining
Event B: Flight leaving on time.
The probability that it will rain is 0.18.
This means that there is a 1 - 0.18 = 0.82 probability of not raining. So [tex]P(A) = 0.82[/tex]
The probability that it will not rain and the flight will leave on time is 0.74.
This means that [tex]P(A \cap B) = 0.74[/tex]
What is the probability that the flight would leave on time when it is not raining?
[tex]P(B|A) = \frac{0.74}{0.82} = 0.902[/tex]
0.902 = 90.2% probability that the flight would leave on time when it is not raining
Rewrite y = square root 25X - 75 + 3 to make it easy to graph using a translation. Describe the graph
Answer:
D
Step-by-step explanation:
y = sqrt(25x-75)+3
y = sqrt(25(x-3))+3
y = sqrt 5(x-3)+3
transformations:
vertically stretched by a factor of 5
right 3 units
up 3 units
D is the best answer
Nam owns a used car lot. He checked the odometers of the cars and recorded how far they had driven. He then created both a histogram and a box plot to display this same data (both diagrams are shown below). Which display can be used to find how many vehicles had driven more than 200{,}000\,\text{km}200,000km200, comma, 000, start text, k, m, end text (kilometers)? Choose 1 answer: Choose 1 answer: (Choice A) A The histogram (Choice B) B The box plot Which display can be used to find that the median distance was approximately 140{,}000\,\text{km}140,000km140, comma, 000, start text, k, m, end text? Choose 1 answer: Choose 1 answer: (Choice A) A The histogram (Choice B) B The box plot
Answer:
(a) The correct option is (A).
(b) The correct option is (B).
Step-by-step explanation:
Nam collected the data for the distance traveled by all the cars in his car lot.
(a)
A histogram is a bar graph representing the distribution of a random variable. The height of the bars of the histogram represents the frequency for a specific interval.
If Nam wants to know how many vehicles had driven more than 200,000 km, the histogram would be the best display of this data. This is because the histogram shows the frequency for various interval values.
The correct option is (A).
(b)
A boxplot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,
Minimum (shown at the bottom of the chart) First Quartile (shown by the bottom line of the box) Median (or the second quartile) (shown as a line in the center of the box) Third Quartile (shown by the top line of the box) Maximum (shown at the top of the chart).So, if Nam wants to find whether the median distance was approximately 140,000 km, a box plot would be a better choice. This is because the box plot represents the median of the data by a line within the box.
The correct option is (B).
Answer: For the first one is A second one is B
Step-by-step explanation: I took the khan test. UwU♡
Please help. I’ll mark you as brainliest if correct!
Answer:
When x = -1/4 and when x = -15/4
Step-by-step explanation:
The x intercept will be when f(x)=0, so
0 = 4|x+2| -7
7 = 4|x+2|
|x+2|=7/4 here you have to cases
case 1
x+2=7/4
x=7/4-2
x=-1/4 = -0.25
case 2
x+2 = -7/4
x = -2-7/4
x = -15/4 = -3.75
A researcher recruited 55 adults and tested their ability to remember a list of words. For each participant, the researcher counted the number of words correctly recalled and recorded their age (in years).
HYPOTHESIS
The research hypothesis is that age is related to memory performance.
This hypothesis is:__________.
a. directional
b. non-directional
Answer:
b. non-directional
Step-by-step explanation:
A directional hypothesis can be described as a hypothesis which predicts the direction of impact, either positive or negative, of one variable, especially independent variable, on the other variable which is known as an independent variable. For example, the hypothesis "age reduces memory performance" is a directional hypothesis. The reason is that "reduces" show the direction that age has a negative effect on memory performance.
On the other hand, non-directional hypothesis can be described as a hypothesis that does not predict the direction of impact but only states the relationship between two variables. For example, the research hypothesis is in the question that "age is related to memory performance" is non-directional hypothesis. This because the word "related" in the hypothesis only indicate that there is a relationship between the two variables, not the direction of effect of one variable on the other.
Please help me with this math problem, urgent please
Answer:
see below
Step-by-step explanation:
To find the x intercept set y =0 and solve for x
6x+5y = -30
6x = -30
Divide by 6
x = -30/6 = -5
The x intercept is (-5,0)
To find the y intercept set x =0 and solve for y
6x+5y = -30
5y = -30
Divide by 5
y = -30/5 = -6
The y intercept is (0,-6)
To find the x-intercept set y =0. Solve for x.
6x+5y=-30
6x+5(0)=-30
6x+0=-30
6x=-30
x=-30/6
x=-5
The x-intercept is at (-5, 0)
To find the y-intercept set x =0. Solve for y.
6x+5y=-30
6(0)+5y=-30
0+5y=-30
5y=-30
y=-30/5
y=-6
The y-intercept is at (0, -6)
Graph the line y=-2x+5
Hope this helps!! :)
What is the answer to this question–1 × –5?
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
Answer:
5
Step-by-step explanation:
Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this
-6 × 7
Then the answer will be -42 because there is only one negative
determine the slope of a line with the equation 6x+2y-4=0
A DJ charges a booking fee of $100 and an hourly rate. He made $250 in 5 hours. Which equation shows the amount the DJ charges per hour?
WILL GIVE BRAINLIEST 4 FIRST ANSWER.
When converted to speeds, which list is in order from slowest to fastest?
A: 17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
B: 17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
C: 33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
D: 60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes
Answer:
c
Step-by-step explanation:
you should divide the distance on time
so
33/6=5.5
26/4=6.5
60/8=7.5
17/2=8.5
you can see answer in this order in c
Answer:
Answer:
c
Step-by-step explanation:
you should divide the distance on time
so
33/6=5.5
26/4=6.5
60/8=7.5
17/2=8.5
you can see answer in this order in c
Step-by-step explanation:
Is (-3,2) a solution of 7x+9y>-3
Yes or no
Please help :))
Answer:
(-3,2) is not a solution.
Step-by-step explanation:
The solution of a linear inequality in two variables like [tex]Ax + By > C[/tex] is an ordered pair [tex](x, y)[/tex] that produces a true statement when the values of x and y are substituted into the inequality.
To find if (-3,2) is a solution of [tex]7x+9y>-3[/tex], you must substitute this point into the inequality.
[tex]7\left(-3\right)+9\left(2\right)>-3\\\\-21+18>-3\\\\-3>-3[/tex]
Because -3 is not greater than -3, (-3,2) is not a solution.
Answer:
No
Step-by-step explanation:
Khan academy
Ravi's age is six times that of Gaurav's. After 8 years Ravi will be twice as old as Gaurav. What are their present ages?
Answer:
10 and 2
Step-by-step explanation
Nitesh is currently 10 and Ravi is currently 2
(2 times 5 is 10)
in 2 years Nitesh will be 12 and Ravi will be 4
(4 times 3 is 12)
Simplify (4.5)(5)(-2)
Answer:
[tex] - 45[/tex]
[tex]2.25( - 2) = - 45 \\ - 45[/tex]
Excell Computers promptly shipped two servers to its biggest client. The company profits RM5,000 on each one of these big systems. The shipping worker randomly selected the system without replacement that were delivered from 15 computers in stock. The system contain 4 refurbished computer, with 11 new computers in the warehouse.
If the client gets two new computers, Excell earns RM10,000 profit. If the client gets a refurbished computer, it’s coming back for replacement and Excell must pay the RM400 shipping fee, with leaves RM9,600 profit. If both computers shipped are refurbished, consequently the client will return both and cancel the order. As a result, Excell will be out any profit and left with RM8,000 in shipping cost. Let X be a random variable for the amount of the profit earned on the order.
Answer:
$9215.24
Step-by-step explanation:
Total Number of Computers=15
Number of New=11
Number of Refurbished Computers=4
P(New)=11/15P(Refurbished)=4/15[tex]P(NN)=\frac{11}{15} \times \frac{10}{14} = \frac{11}{21}\\P(NR)=\frac{11}{15} \times \frac{4}{14} = \frac{22}{105}\\P(RN)=\frac{4}{15} \times \frac{11}{14} = \frac{22}{105}\\P(RR)=\frac{4}{15} \times \frac{3}{14} = \frac{2}{35}[/tex]
The probability of one new and one refurbished =P(NR)+P(RN)
[tex]=\frac{22}{105}+ \frac{22}{105}\\=\frac{44}{105}[/tex]
Let X be the amount of profit earned on the purchase. The probability distribution of X is given as:
[tex]\left|\begin{array}{c|c|c|c|c}$Profit(X)& NN=\$10000 &NR=\$9600& RR=-\$800\\$P(X)&\dfrac{11}{21}&\dfrac{44}{105}&\dfrac{2}{35}\end{array}\right|[/tex]
(b) Expected Profit
[tex]\text{Expected Profit}=\sum X_iP(X_i)\\=(10000 \times \dfrac{11}{21}) +(9600 \times \dfrac{44}{105}) + (-800 \times \dfrac{2}{35})\\=\$9215.24[/tex]
The average profit of the store on the order is $9215.24.
A high school track is shaped as a rectangle with a half circle on either side.Jake plans on running four laps. How many meters will Jake run? Use 3.14 for Pi.
Answer:
if you go around a track one time thats 400 meters but if you go around 4 times thats 1600 meters, you dont need to use 3.14 pi for this " no offense", i do track and field myself and i do the short distance, which is 100 meters and 200 meter but for for long distance runners they go around the track 4- 8 times so it is 1600 meters is ur answer. and when u go around 8 times, thats 3200 meters.
Step-by-step explanation:
Solve: 4x^-2 – 3x^-1– 1 = 0
Answer:
1, -4
Step-by-step explanation:
4x^-2 – 3x^-1– 1 = 0Let x^-1 = 1/x = y
4y^2 - 3y - 1 = 04y^2 - 4y + y - 1 = 0(y - 1) (4y + 1) = 01. Root 1
y - 1 = 0 y = 11/x= 1x = 12. Root 2
4y + 1 = 04y = -1y = -1/41/x = - 1/4x = -4Which statement best compares the graphs of y = –3xn and y = 3xn?
Answer: choice B
Step-by-step explanation:
The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x-axis.
Answer: B
Step-by-step explanation:
What is the equation of the exponential graph shown?
Answer:
[tex]100(0.5)^{x}[/tex]
Step-by-step explanation:
According to the graph, the y int is at 100
so that is the starting point
Then at 1 it is at 50
[tex]\frac{100}{50}[/tex] is 2 so that means it is reduced by half
Just to make sure, [tex]\frac{50}{25}[/tex] is also /2 so that means it is the slope
Since it is a decay, the slope has to be less than one so you get the reciprecol of 2 to get....
[tex]\frac{1}{2}[/tex]
Answer:f(x)=100(2^x)
Step-by-step explanation:
if you’re good with probability in math 30 please help and answer the question below!!
A six-sided number cube has faces with the numbers 1 through 6 marked on it. What is the probability that a number less than 3 will occur on one toss of the number cube?
a) 1/6
b) 1/2
c) 1/3
d) 2/3
Answer: b) 1/3
Step-by-step explanation:
The numbers LESS THAN 3: 1, 2
[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
How would I start this?
Answer:
(0, ∞)
Step-by-step explanation:
A good place to start is by visualizing what the graph looks like on a number line.
For x > 0, it is an open circle at x=0, and shading to the right extending to infinity.
__
So, the left end of the interval is 0, but 0 is not included in the interval.
The right end of the interval is infinity, but there is no such number, so "infinity" is not included in the interval.
"Not included" means you use round brackets ( ) for the corresponding end of the interval. ("Included" would mean you use square brackets [ ].)
So, the interval 0 < x < ∞ is written in interval notation as ...
(0, ∞)
What is X=
5/6 = 10/2x−3
Answer: x= 23/30
Step-by-step explanation:
[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{2}x -3[/tex] reduce 10/2 to 5 because 10/2 is 5.
5/6 = 5x -3
+ 3 +3
23/6 = 5x divide both sides by 5.
x= 23/30
