Suppose X is a normally distributed random variable with mean 0 and variance 1 (i.e., standard normal).
Compute the following (Hint: you can use the R functions pnorm and qnorm to answer these questions).
P r(X < 1:96)
P r(X > 1:64)
P r(0:5 < X < 0:5) 1% quantile, q:01 and 99% quantile, q:99 ? 5% quantile, q:05 and 95% quantile,
Answers
Answer:
\(P(X <1.96) = 0.975\)
\(P(X >1.64) = 0.0505\)
\(P(0.5 < X < 0.5) = 0\)
Step-by-step explanation:
Given
\(\bar x = 0\) --- Mean
\(\sigma^2 = 1\) --- Variance
Calculate the standard deviation
\(\sigma^2 = 1\)
\(\sigma = 1\)
Solving (a): P(X < 1.96)
First, we calculate the z score using:
\(z = \frac{X - \bar x}{\sigma}\)
This gives:
\(z = \frac{1.96 - 0}{1}\)
\(z = \frac{1.96}{1}\)
\(z = 1.96\)
The probability is then solved using:
\((X < 1.96) = P(z <1.96)\)
From the standard normal distribution table
\(P(z <1.96) = 0.97500\)
So:
\(P(X <1.96) = 0.975\)
Solving (b): P(X > 1.64)
First, we calculate the z score using:
\(z = \frac{X - \bar x}{\sigma}\)
This gives:
\(z = \frac{1.64 - 0}{1}\)
\(z = \frac{1.64}{1}\)
\(z = 1.64\)
The probability is then solved using:
\((X > 1.64) = P(z >1.64)\)
\(P(z >1.64) = 1 - P(z<1.64)\)
From the standard normal distribution table
\(P(z >1.64) = 1 - 0.9495\)
\(P(z >1.64) = 0.0505\)
So:
\(P(X >1.64) = 0.0505\)
Solving (c): P(0.5 < X < 0.5)
This can be split as:
\(P(0.5 < X < 0.5) = P(0.5<X) - P(X<0.5)\)
In probability:
\(P(0.5<X) = 1 - P(X>0.5)\)
\(P(0.5<X) = 1 - [1 - P(X<0.5)]\)
\(P(0.5<X) = 1 - 1 + P(X<0.5)\)
\(P(0.5<X) = P(X<0.5)\)
\(P(0.5 < X < 0.5) = P(0.5<X) - P(X<0.5)\) becomes
\(P(0.5 < X < 0.5) = P(X<0.5) - P(X<0.5)\)
\(P(0.5 < X < 0.5) = 0\)
Related Questions
what is the slope of the line below -3,2 3,2
a. negative
b.undefined
c. positive
d.zero
Answers
Answer:
0
Step-by-step explanation:
let (-3,2) be (x1,y1)
and(3,2)be(x2,y2)
Now,
slope = y2-y1/x2-x1
=2-2/3-(-3)
=0/3+3
=0/6
therefore slope=0
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n
Answers
Answer:
The answer is option AStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6
Substitute the values into the above formula
A(n) = 38 + (n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
a
Step-by-step explanation:
you're welcome!
What are the answers to these questions?
Answers
Step-by-step explanation:
the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.
therefore, for our example here the negative case would be
2.5x - 6.8 = -12.9
which gives us
2.5x = -6.1
x = -6.1/2.5 = -2.44
and the positive case would be
2.5x - 6.8 = 12.9
and that gives us
2.5x = 19.7
x = 19.7/2.5 = 7.88
I really need help, please help me.
Answers
Answer:
96 degrees
Step-by-step explanation:
Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:
y+84=180
y=180-84=96
Hope this helps!
please fast if could
Answers
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
Three students were given the expression shown and were asked to take a common factor out of two of the terms.
4-9x+21
Chang: 4-3(3x+7)
Chang’s expression is ___ because _______.
Benjamin: 4+3(3x+7)
Benjamin’s expression is ___ because ________.
Habib: 4+12x
Habib’s expression is ___ because ________.
Equivalent Expression
The correct simplification of this expression _____.
please help me omg
Answers
Answer:
Step-by-step explanation:
What part of an hour passes from 3:12 p.m. to 5:30 p.m.?
Answers
Answer:
2.3 hours
Step-by-step explanation:
From 3:12 pm to 4:12 pm, one hour passes.
From 4:12 pm to 5:12 pm, another hour passes.
From 5:12 pm to 5:30 pm, there are 18 minutes that pass.
Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.
To convert this to a fraction, we can write:
2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours
So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.
What is the translation from
a) shape X to shape Z?
b) shape Z to shape X?
Answers
The translation form of each shape is given as follows:
a) X to Z: (x, y) -> (x + 5, y + 2).
b) Z to X: (x, y) -> (x - 5, y - 2).
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the composition of translations, we add the coordinates, hence:
-2 + 7 = 5.5 - 3 = 2.Hence the rule from X to Z is given as follows:
(x, y) -> (x + 5, y + 2).
From Z to X, we have the inverse rule, hence:
(x, y) -> (x - 5, y - 2).
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Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 15 calls per hour. The arrival rate is 30 calls per hour.
How many extension lines should be used if the company wants to handle 90% of the calls immediately?
fill in the blank 1
lines should be used
What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places.
L = fill in the blank 2
What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places.
fill in the blank 3
%
Answers
The various answers to the question are:
To answer 90% of calls instantly, the organization needs four extension lines.The average number of extension lines that will be busy is FourFor the existing phone system with two extension lines, 34.25 % of calls get a busy signal.How many extension lines should be used if the company wants to handle 90% of the calls immediately?a)
A number of extension lines needed to accommodate $90 in calls immediately:
Use the calculation for busy k servers.
\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)
The probability that 2 servers are busy:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
Hence, two lines are insufficient.
The probability that 3 servers are busy:
Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)
Thus, three lines are insufficient.
The probability that 4 servers are busy:
Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)
Generally, the equation for is mathematically given as
To answer 90% of calls instantly, the organization needs four extension lines.
b)
The probability that a call will receive a busy signal if four extensions lines are used is,
\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)
Therefore, the average number of extension lines that will be busy is Four
c)
In conclusion, the Percentage of busy calls for a phone system with two extensions:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.
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cos (x + 16) = sin(3x – 2)
Answers
Answer:
x = 19
Step-by-step explanation:
So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°
Use this idea to set up an equation.
x + 16 + 3x - 2 = 90
Combine like terms.
4x + 14 = 90
Subtract 14.
4x = 76
Divide by 4.
x = 19
x = 19
If you are kooking for the angles:
x + 16
= 19 + 16
= 35
and
3x - 2
= 3(19) - 2
= 57 - 2
= 55
Check: 35 + 55=90
Also,
cos35 = sin55
Cos x + cos 16 = sin 3x - sin 2
Sin 2 + cos 16 = sin 3x - cos x
Sin 2 + cos 16 = x(sin 3 - cos 1)
0.0902 + (-0.9576) = x(0.1411-0.5403)
−0.8674 = −0.3992x
-0.3992 -0.3992
X = 2.17
help me solve this queston
Answers
TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.
And the correct graph is D.
To represent the given problem as a system of equations, we can use the following information:
John is 70 years younger than Sharon: j = s - 70
Sharon is 4 times as old as John: s = 4j
Let's plot the graph for this system of equations:
First, let's solve equation (2) for s:
s = 4j
Now substitute this value of s in equation (1):
j = s - 70
j = 4j - 70
3j = 70
j = 70/3
Substitute the value of j back into equation (2) to find s:
s = 4j
s = 4(70/3)
s = 280/3
The solution to the system of equations is j = 70/3 and s = 280/3
In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.
Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.
And the correct graph is D.
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Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
Answers
Surface area = 6 * side length^2
In this case, the surface area of the cube is 96ft², so you can set up the equation:
96ft² = 6 * side length^2
Solving for side length gives:
side length = sqrt(96ft² / 6) = 4ft
The volume of the cube is side length^3, so the volume of the cube is 4ft^3 = 64ft^3.
Therefore, the correct answer is C) 84.06ft³.
Salena has twice as many DVDs as Jolene,and Jolene has one third as many as Brodie.What fraction of the total DVDs has Salena?
Answers
Answer:
let jolene's dvd be x
2x+x+3x= total dvds = 6x
2x/6x=1/3
Salena has 1/3 of the total dvds
PHOTO ATTACHED PLESE HELPPPP!!!!!!!!!!!!!!
Answers
Answer:
\(5x^2 + 3x - 2\)
This answer is correct because I simplified using like terms.
Step-by-step explanation:
Subtracting Polynomials
They key to subtract, multiply, add, and divide polynomials is by using like terms. Like terms are values with the same bases. For example :
\(ax^2\) and \(2ax^2\) are like terms because they have the base \(ax\)
Step 1: Move like terms together
First, let's remove all parenthesis:
\((3x^2 + 9x-6)-(2x^2-4x^2+6x-4)\\\\= 3x^2+9x-6-2x^2+4x^2-6x+4\)
Now let's move all like terms together:
\(3x^2+9x-6-2x^2+4x^2-6x+4= \\3x^2-2x^2+4x^2+9x-6x-6+4\)
Step 2: Simplify
Now we can add and subtract the like terms like we do in any other problem
\(3x^2-2x^2+4x^2+9x-6x-6+4 = \\5x^2+3x-2\)
Step 3: Explaining your answer
Just say: "This answer is correct because I simplified using like terms"
-Chetan K
A 3-gallon bucket of paint costs $111.12. What is the price per quart?
Answers
Answer:
9.26 per quart
Step-by-step explanation:
A 3-gallon bucket of paint costs $111.12.
Find the price of per quart.
3 gallons equal 12 quarts. We divide 111.12 for 12 quarts by 12:
111.12 / 12 = 9.26
Missed 7 problems on math test got 95% how many questions were on test
Answers
Answer:
I think there is 140 questions
Find the area of this problem
Answers
The area of the kite is A = 48 units²
Given data ,
Let the area of the kite be represented as A
Now , the value of A is
Let the first diagonal of the kite be d₁ = 12 units
Let the second diagonal of the kite be d₂ = 8 units
Now , Area of kite = ( 1/2 ) d₁ x d₂
On simplifying , we get
A = ( 1/2 ) ( 12 ) ( 8 )
A = 48 units²
Therefore , the value of A is A = 48 units²
Hence , the area of the kite is A = 48 units²
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Find the area of the triangle.
3).
Answers
Answer:
86.60254
Step-by-step explanation:
30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)
A jar has marble ms in these three colors only: 7 green, 10 blue, 3 red.
What is the probability of randomly choosing a green marble, after choosing (and keeping) a red marble?
Answer with a percentage rounded to the nearest tenth.
Answers
The probability of randomly choosing a green marble after you have chosen red is 4.4%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given
A jar has 20 marbles: 3 green, 12 blue, 5 red.
Probability;
In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.
The total number of marbles = 20
The number of green marbles= 3
The number of blue marbles = 12
The number of red marbles = 5
The probability of choosing a red marble = Number of red marbles / Total number of marbles
= 5/20
The probability of choosing a green marble is = Number of green marbles / New total number of marbles
= 3/19
Therefore,
The probability of randomly choosing a green marble after you have chosen red is;
= 5/20 * 3/19
= 3/68
percentage = 3/68 * 100 = 4.4%
Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%
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how do i know which one?
Answers
The inequality value that would be able to show/x/ ≤ 5 is option A
What is inequality?
In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.
The symbol that we have is telling us that the value of the x would be less than or it would be seen to be equal to five.
We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A
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Triangle FGH, with vertices F(-5,-7), G(-2,-5), and H(-6,-2), is drawn inside a rectangle, as shown below.
Answers
The area of the triangle FGH is equal to 13√10 unit²
Given that the vertices;
F(-5,-7), G(-2,-5), and H(-6,-2)
We have to find the area of the triangle as;
Area of triangle = 1/2bh²
Here,
Area of triangle FGH = 1/2 (GH) (FG)²
Now,
Length of FG = √26
Length of GH = √10
Then,
Area of triangle FGH = 1/2 (GH) (FG)²
Area of triangle = 1/2 × √10 × √26²
Area of triangle = 1/2 × √10 × 26
Area of triangle FGH = 13√10
Therefore,
The area of the triangle FGH = 13√10 unit²
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Say you buy 4 tomatoes and 5 carrots and you spend 476 dollars how much did they both cost?
Answers
One carrot would cost $23.8
That means that in total they would both cost $23.8 for each carrot or tomato
What is the slope of the line that passes through the points ( 9 , 5 ) (9,5) and ( 21 , − 5 ) (21,−5)? Write your answer in simplest form.
Answers
Answer:
-5/6
Step-by-step explanation:
(9, 5) and (21, -5)
slope = m = (difference in y)/(difference in x)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Answer: -5/6
The slope of the line that passes through points (9,5) and (21,-5) is -5/6.
We can use the two-point formula to find the slope for the given line. The formula is as follows:
(y2 - y1) = m*(x2 - x1)
Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.
In the given case:
x1=9, x2=21
y1=5, y2=-5
Using these values in the two-point formula, we get:
(-5-5)=m*(21-9)
-10=m*12
m=-10/12
m=-5/6
Hence the slope of the line is -5/6.
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The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
What is the length of AD?'
Use the given information to complete the worksheet.
Thank you!
Answers
The length of side AD is,
⇒ AD = 16
We have to given that;
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
Since, Volume of right triangular prism is,
V = 1/2 (bh) x L
Substitute all the values we get;
V = 1/2 (22 × 11) × AD
1936 = 121 × AD
AD = 16
Thus, The length of side AD is, 16
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3
2
Show gred
1
16
-5
4
1 2
3
4
5 6
3 -2 -1
11
-5
-6
- x2. on
sin - cos - tan-
+ - X + / +
log-e? 10
-
10n
Show less
Answers
Answer:
The gradient of the graph below is \(\mathbf{\frac{3}{2} }\)
Step-by-step explanation:
We need to calculate the gradient of the graph
The gradient of graph is actually slope of the graph.
The slope of graph can be calculated using formula: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)
Taking any 2 points on graph i.e
(1,0) and (-1,-3)
We have \(x_1=1, y_1=0, x_2=-1,y_2=-3\)
Putting values and finding gradient:
\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-3-0}{-1-1}\\Slope=\frac{-3}{-2}\\Slope=\frac{3}{2}\)
So, The gradient of the graph below is \(\mathbf{\frac{3}{2} }\)
6 erasers cost $6.60. Which equation would help determine the cost of 3 erasers
Answers
I think its just 6.60 divided by six, thats how many each one costs, then multiply it by 3
Hope this helps :)
Answer:
3.3
Step-by-step explanation:
because you can divide 6.60 by 6 which is 1.1 then multiply it by 3
1/2x - 5+ 2/3 x= 7/6x+4
Answers
in the pic....................Complete the puzzle by selecting the puzzle piece that contains equivalent expression.
Answers
Simplifying the given expression, we have the following:
\(\begin{gathered} \frac{(2x^2y^3)^5}{(4x^4y)(y^{12})} \\ =\frac{2^5x^{2\cdot5}y^{3\cdot5}}{4x^4y^{1+12}} \\ =\frac{32x^{10}y^{15}}{4x^4y^{13}} \end{gathered}\)Reducing the fraction to its lowest term we get
\(\begin{gathered} \frac{32x^{10}y^{15}}{4x^4y^{13}} \\ =8x^{10-4}y^{15-3} \\ =8x^6y^{12} \\ \\ \text{Therefore, the equivalent expression of the given is} \\ \frac{(2x^2y^3)^5}{(4x^4y)(y^{12})}=8x^6y^{12} \end{gathered}\)Let u = 2i + 3j, v = –i, and w = 5i – 6j. What is the magnitude of 2(u – v + w)?
10.0
13.4
17.1
21.6
Answers
2u - 2v + 2w
(4i+3j) - (-2i) + (10i - 12j)
4i + 2i + 10i = 16i
3j - 0j -12j = -8j
16 - 8j
magnitude = √( 16²+(-8)² ) = 17.1
Answer:
C. 17.1
Step-by-step explanation:
edge
Share #720 among A, B and C in the ratio 2:3
Answers
Answer:
A will receive 288, B will receive 432, and C will receive 144.
Step-by-step explanation:
The total ratio of the parts is 2+3=5. This means that the whole amount represents 5 parts.
To find the size of one part, we can divide the total amount by the total number of parts:
One part = 720/5 = 144
Now that we know the size of one part, we can use the ratio to find the amounts that A, B, and C will receive:
A will receive 2 parts: 2 × 144 = 288
B will receive 3 parts: 3 × 144 = 432
C will receive 1 part: 1 × 144 = 144
Therefore, A will receive 288, B will receive 432, and C will receive 144.