Let X be a normal random variable with mean 3 and variance 4. (a) Find the probability P(2 < X < 6). (b) Find the value c such that P(X > c) = 0.33. (c) Find E[X2 ]. Hint: You can integrate with the density function, but it is quicker to relate E[X2 ] to the mean and variance.
Answers
Answer:
a) the probability of (2 < X < 6) is 0.6247
b) the value of c is 3.878
c) the value of E[ x² ] is 13
Step-by-step explanation:
Given that;
mean μ = 3
variance = 4
standard deviation s = √variance = √4 = 2
(a) Find the probability P(2 < X < 6)
P(2 < X < 6) = p( (x - μ / s ) < z < (x - μ / s ) )
= p( (2 - 3 / 2 ) < z < (6 - 3 / 2 ) )
= p( -0.5 < z < 1.5)
from z-score table, 1.5; z = 0.9332 and -0.5; z = 0.3085
so
P(2 < X < 6) = 0.9332 - 0.3085 = 0.6247
Therefore, the probability of (2 < X < 6) is 0.6247
b) Find the value c such that P(X > c) = 0.33
with p-value = 0.33, the corresponding z -score to the right is 0.439
we know that;
z = x - μ / s
we substitute
0.439 = x - 3 / 2
x - 3 = 2 × 0.439
x - 3 = 0.878
x = 0.878 + 3
x = 3.878
Therefore, the value of c is 3.878
c) Find E[ x² ].
Variance = E[ x² ] - [ mean ]²
E[ x² ] = Variance + [ mean ]²
we substitute
E[ x² ] = 4 + [ 3 ]²
E[ x² ] = 4 + 9
E[ x² ] = 13
Therefore, the value of E[ x² ] is 13
The distribution follows a normal distribution.
\(\mathbf{P(2 < x < 6) =0.6247}\)The value of c is 3.878The value of \(\mathbf{E(x^2) }\) is 13The given parameters are:
\(\mathbf{\mu = 3}\) --- mean
\(\mathbf{\sigma^2= 4}\) --- variance
(a) P(2 < x < 6)
Start by calculating the standard deviation
\(\mathbf{\sigma = \sqrt{\sigma^2}}\)
This gives
\(\mathbf{\sigma = \sqrt{4}}\)
\(\mathbf{\sigma =2}\)
Calculate the z-scores for x = 2 and 6
\(\mathbf{z = \frac{x - \mu}{\sigma}}\)
So, we have:
\(\mathbf{z = \frac{2 - 3}{2} = -0.5}\)
\(\mathbf{z = \frac{6 - 3}{2} = 1.5}\)
So, the probability becomes
\(\mathbf{P(2 < x < 6) = P(-0.5 < z < 1.5)}\)
Using z table of probabilities, we have:
\(\mathbf{P(2 < x < 6) =0.9332 - 0.3085}\)
\(\mathbf{P(2 < x < 6) =0.6247}\)
(b) Calculate c if P(X > c) = 0.33
Start by calculating the z-score for p-value = 0.33
From the z table, z = 0.439 when p-value = 0.33
Recall that:
\(\mathbf{z = \frac{x - \mu}{\sigma}}\)
So, we have:
\(\mathbf{0.439 = \frac{x - 3}{2}}\)
Multiply both sides by 2
\(\mathbf{0.878= x - 3}\)
Add 3 to both sides
\(\mathbf{3.878= x}\)
Rewrite as:
\(\mathbf{x = 3.878}\)
Replace x with c
\(\mathbf{c = 3.878}\)
The value of c is 3.878
(c) Calculate E[x²]
The variance of a dataset is:
\(\mathbf{\sigma^2 =E(x^2) - \mu^2}\)
Substitute known values
\(\mathbf{4 =E(x^2) - 3^2}\)
\(\mathbf{4 =E(x^2) - 9}\)
Add 9 to both sides
\(\mathbf{13 =E(x^2) }\)
Rewrite as:
\(\mathbf{E(x^2) = 13 }\)
Hence, the value of \(\mathbf{E(x^2) }\) is 13
Read more about normal random variables at:
https://brainly.com/question/11395972
Related Questions
need help with #10 :’)
the # is “Which of the following expressions is equivalent to 42 + 63?
A- 3(15+21)
B- 6(7+9)
C- 7(6+9)
D- 14(3+3)
8
Answers
Answer:
the answer is c
Step-by-step explanation:
first add : 42+63=105
so you need to solve the expressions until you find the one that equal the same amount.
start with the problem in the parenthesis then multiply.
you will find that C equals 105
6+9=15
15×7=105
Olivia buys 0.5 pounds of ricotta cheese and 0.25 pounds of parmesan cheese. The parmesan cheese costs $5 more than the ricotta cheese. She pays a total of $9.50. What is the cost for a pound of parmesan? What is the cost for a pound of ricotta? NEED ANSWER QUICKLY.
Answers
Answer:
$16
Step-by-step explanation:
let x = cost of ricotta cheese
let x + 5 = cost of parmesan cheese
.5x + .25(x+5) = $9.5
solve this and we get x =11 (cost per pound for ricotta)now we plug that value back into x + 5 to find the cause of the cost of parmesan cheese
11 +5 = 16y = 16
The cost of ricotta cheese will be $11. And the cost of parmesan cheese will be $16.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Olivia buys 0.5 pounds of ricotta cheese and 0.25 pounds of parmesan cheese. The parmesan cheese costs $5 more than the ricotta cheese. She pays a total of $9.50.
Let 'x' be the cost of ricotta cheese. Then the cost of parmesan cheese will be (x + 5). Then the equation is given as,
0.5x + 0.25 · (x + 5) = $9.5
Simplify the equation, then we have
0.5x + 0.25 · (x + 5) = $9.5
0.5x + 0.25x + 1.25 = $9.5
0.75x = 8.25
x = $11
Then the cost of parmesan cheese is given as,
x + 5 = $11 + 5
x + 5 = $16
The cost of ricotta cheese will be $11. And the cost of parmesan cheese will be $16.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Find the degree of the monomial.4.5
8a b5
Answers
Answer: 17a
Step-by-step explanation: additon
Find the x-intercepts of the graph.
20
X =
10
y
2
4
y=-3x² + 14x + 5
], x=
X
X
![Find the x-intercepts of the graph.20X =10y24y=-3x + 14x + 5], x=XX](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/dDEGNMyDp7oZrHm18ZgoSai0ge5ds6wn.png)
Answers
The x-intercept of the function is (-1/3, 0) and (5, 0)
Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,
So to find the x-intercept put y = 0,
Therefore,
-3x²+14x+5 = 0
-3x²+15x-x+5 = 0
-3x(x-5)-1(x-5) = 0
(-3x-1)(x-5) = 0
Therefore,
x = -1/3 and x = 5
Hence the x-intercept of the function is (-1/3, 0) and (5, 0)
Learn more about x-intercept click;
https://brainly.com/question/14180189
#SPJ1
![Find the x-intercepts of the graph.20X =10y24y=-3x + 14x + 5], x=XX](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/0HasbxTlGSTagb3QABQu3VKIuhFwh8Xw.png)
I will give braniest to the person that answers all of the given questions
A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 11 minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 13 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
a. Write the equation. Let d be the distance of the flowerbed from the hive
Answers
Answer:
Below in bold.
Step-by-step explanation:
a. Distance = speed * time
d = st
So substituting in the given values:
d = 20t where t is the time it takes to travel from the hive to the flowerbed.
The total time that the bee is inflight = 13-11 = 2 minutes
= 120 seconds.
So for the return flight the time taken is (120-t) seconds.
So d = 16(120 - t).
and we can find the distance from the hive to flowerbed by solving the the 2 equations highlighted.
b, d = 20t
d = 16(120 - t).
As both right side expressions are equal to d we can write:
20t = 16(120 - t)
20t = 1920 - 16t
20t+ 16t = 1920
t = 1920/36
= 53.33 seconds.
So the distance from hive to flowerbed
= 53.33 * 20
= 1066.67 feet.
Can you please find and solve the unknown variable.
Answers
The value of x is; x = 3.14
Here, we have,
from the given diagram, we get,
there is a right angle triangle.
we have to find the value of x.
we know that,
Let the angle be θ , such that
cos θ = base / hypotenuse
here, we get,
cos 17 = 3/x
so, we have,
0.956 = 3/x
so, x = 3.14
Hence, The value of x is;x = 3.14
To learn more about trigonometric relations click :
brainly.com/question/14450671
#SPJ1
Goran is riding his bike. The number of revolutions his wheels make varies directly with the distance he travels. See the graph below.
Answers
Answer: Add a graph and I'll answer it.
In the figure below, trapezoid WXYZ is isosceles, with WZ XY.
If mXWZ = 125° and mWXZ = 27°, what is mXZY?
A.
27°
B.
35°
C.
20°
D.
55°
Answers
Answer: the answer is 27 degrees .
What is volume of cube 3 2/3 all sides
Answers
Solve the system of equations by graphing
Answers
Answer:
Here's a graph to help you solve this answer:
Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 + ab + b2)
Answers
Answer:
Use the distributive property to multiply the factors on the right side of the equation.
Simplify the product by combining like terms.
Show that the right side of the equation can be written exactly the same as the left side.
Show that the right side of the equation simplifies to a cubed minus b cubed.
Step-by-step explanation:
The difference of two cubes identity a³ - b³ = (a - b)(a² + ab + b²) has been proved using; distributive property of algebra.
We want to prove that;
a³ - b³ = (a - b)(a² + ab + b²)
Now, to solve this we need to understand the distributive property of algebraic functions.This distributive property means distributing an item over others in a bracket. For example; a(b + c) = ab + acApplying this same distributive property to our question gives us;(a - b)(a² + ab + b²) = a(a² + ab + b²) - b(a² + ab + b²)
Multiplying out the brackets gives us;
a³ + a²b + ab² - a²b - ab² - b³
Like terms cancel out to give us;
a³ - b³.
This is same as the left hand side of our initial equation and thus it has been proved.
Read more at; https://brainly.com/question/2747971
The following are ages of 17 of the signers of the Declaration of Independence.
49, 34, 42, 43, 39, 36, 50, 44, 45, 33, 34, 27, 33, 69, 46, 50, 41
Send data to calculator
Find 25th and 80th percentiles for these ages.
(If necessary, consult a list of formulas.)
(a) The 25th percentile:
The 80th
percentile:
Answers
Answer:
Step-by-step explanation:
The problem specifies that you may use a calculator. The formula, as reference, is:
You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).
So the answers:
25th percentile is 34.
80th percentile is 48.4.
prime factorization of the following numbers in exponential form 48prime factor of 32
Answers
32: 2 x 2 x 2 x 2 x 2, which can also be written 32 = 2⁵.
A scale model of a sofa has a scale of 1 : 25. The map is 3 inches long. How long is the actual sofa?
Answers
Answer:
75 inches
Step-by-step explanation:
1 * x = 25 * 3
x = 75
Therefore, the actual length of the sofa is 75 inches.
A house was valued at $299,000 . Over several years, the value decreased by, 9% giving the house a new value.
(a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal.
(b) Use your answer in part (a) to determine the new value.
Answers
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
Step-by-step explanation:Make A Plan:
A) - Calculate the Percentage of the Value Remaining After the Decrease
B) - Calculate the NEW VALUE of the house
SOLVE THE PROBLEM:
A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE
100% - 9% = 91%
As A DECIMAL:0.91
B) - Calculate the NEW VALUE of the house:
NEW VALUE = OLD VALUE * REMAINING PERCENTAGE
NEW VALUE = 299,000 * 0.91
Draw the conclusion:
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
I hope it helps!
Economists predict that Americans will spend $1,180 on Summer Vacation in 2015, this is up 3.4% from 2014. What did Americans spend in 2014?
Answers
With the help of percentage increase information, we conclude that, Americans spent approximately $1,141.31 on summer vacation in 2014.
What is percenatge increase?
Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.
To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.
Let X be the amount spent in 2014.
We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:
3.4% = 0.034 (as a decimal)
We also know that the amount spent in 2015 is $1,180.
Using this information, we can set up an equation:
X + 0.034X = 1180
Simplifying the left side:
1.034X = 1180
Dividing both sides by 1.034:
X = 1141.31
So Americans spent approximately $1,141.31 on summer vacation in 2014.
To learn more about percentage increase visit:
https://brainly.com/question/28398580
#SPJ1
A professor obtains SAT scores and freshman GPA for a group of 15 college students with the hope that she can predict GPA using SAT scores. Which hypothesis test would be appropriate for this example
Answers
The hypothesis test analyzes the null and alternative hypothesis of the
plausibility of a correlation between the SAT scores and GPA.
The hypothesis test that would be appropriate is a hypothesis test that checks that the slope of the regression line is not zero.Reasons:
The data collected by the professor = The scores of the college students
The type of scores collected = SAT scores, and GPA scores
The test that would be appropriate for the example, is the test for the
existence of a significant linear relationship between the input variable
(the SAT scores) and the output variable (the GPA)
The test is known as the test for the slope of the regression line
The equation of the regression line is; Y = B₀ + B₁·X
Where;
Y = The value of the GPA score (The dependent variable)
X = The value of the SAT score (The independent variable)
The test aims to check that the value the slope of the regression line is
much different from zero, such that there exist a correlation.
Learn more about hypothesis test for linear regression here:
https://brainly.com/question/13938204
NEED HELP ASAP a bag contains four green marbles,six white marbles, and ten red marbles. One marble is picked at random from the bag. What is the probability of picking a white marble?
Answers
Answer:
3/10
Step-by-step explanation:
add all the marbles together4+6+10
=20
probability of picking a white marble is6/20
=3/10
The cost in dollars y of producing x computer
desks is given by y = 20x + 3000
х
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $4300. (HintFind x when y = 4300)
a. Complete the table.
х
100
200
300
y
b. For $4300, computer desks can be produced.
Answers
Answer:
Step-by-step explanation:
a. table
x = 100,y = 20*100+3000 = 2000+3000 = 5000
x = 200,y = 20*200+3000 = 4000+3000 = 7000
x = 300,y = 20*300+3000 = 6000+3000 = 9000
b：
y = 4300
4300 = 20x+3000
20x = 4300-3000
20x = 1300
x = 1300/20
x = 65
so 65 computer desks can be produced.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.
(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.
(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.
(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
The triangle similarity criteria are:
AA (Angle-Angle)SSS (Side-Side-Side)SAS (Side-Angle-Side)(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.
12/8 = 9/6
1.5 = 1.5
(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.
(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.
14/10 = 21/15
1.4 =
(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.
SMK = 90⁰, 60⁰, 30⁰
QTR = 90⁰, 30⁰, 60⁰
Learn more about similar triangles here: brainly.com/question/27996834
#SPJ1
Clarance has a 25% off coupon for a tune-up at Quick Service Auto Repair. If a tune-up is regularly $50, what is the sale price?
Answers
Answer:
$37.50
Step-by-step explanation:
50*.25=12.50
Take $50 - 12.50 = 37.50
Kensy has $9 and makes $3 every day. Jose has $2 and makes $4 every day. When will they have the same amount of money
A. 5 days
B. 6 days
C. 7 days
D. 10 days
Answers
7 DAYS
Find all the values in the interval (0.1, 0.4]
Answers
Answer:
infinite values
Step-by-step explanation:
there are infinite values between 0.1 and 0.4
0.234234,0.3,0.2743843 etc.
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
Read more about tangent lines at
https://brainly.com/question/21595470
#SPJ1
A cell phone plan charges $49.75 per month plus $13.98 in taxes, plus $0.60 per minute for calls beyond the 700-minute monthly
limit. Write a piecewise-defined function to model the monthly cost C (x) (in $) as a function of the number of minutes used for the
month.
Answers
49.95 + 14.02 = 63.97
c(m) = 63.97 if 0 < m ≥ 600
c(m) = 0.4m + 63.97 if m > 600
I need help with 8 and 11 show ur work and check it
Answers
Answer:
c=15. 11 is x = 35
Step-by-step explanation:
Start by subtracting 10 from 25
25-10 = 15
Check:
10 + 15 = 25
Therefore, the answer is c = 15
20 + 15 is 35
Check with 35 - 15 = 20
Therefore, x = 35 is the answer
Answer:
15
Step-by-step explanation:
do 25-10=15
8 times 4 = ( x times 7) minus (x times 3).
please help
Answers
Answer:
8
Step-by-step explanation:
x * 7 and x * 3 become as follows
8 * 4 = 7x - 3x
32 = 4x
divide 4 on both sides
8
What is the sum of 7/12 + 4/5
Answers
83/60
Step-by-step explanation:Hi there !
⁵⁾7/12 + ¹²⁾4/5 =
= 35/60 + 48/60
= (35 + 48)/60
= 83/60
Good luck !
Answer right and get branliest
Answers
Answer:
8 outfits
Step-by-step explanation:
Each number represent a different shirt and each letter represents a different skirt:
1 2 3 4
A B
Outfits:
1A 2A 3A 4A
1B 2B 3B 4B
(hope this helps, i don't really know how to explain it)
Answer:
I got 8!
Step-by-step explanation:
A fancy restaurant put dishes of butter at each table. They divided 4/5 of a kilogram of butter evenly to put 1/5 of a kilogram in each dish. How many butter dishes did they fill?
Answers
Answer: 4
This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.
4/5 ÷ 1/5
Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:
4/5 x 5
To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.
You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.
Hope this helps!