If y has moment-generating function m(t) = e 6(e t −1) , what is p(|y − µ| ≤ 2σ)?

Answers

Answer 1

Since [tex]\mathrm M_Y(t)=e^{6(e^t-1}[/tex], we know that [tex]Y[/tex] follows a Poisson distribution with parameter [tex]\lambda=6[/tex].

Now assuming [tex]\mu,\sigma[/tex] denote the mean and standard deviation of [tex]Y[/tex], respectively, then we know right away that [tex]\mu=6[/tex] and [tex]\sigma=\sqrt6[/tex].

So,

[tex]\mathbb P(|Y-\mu|\le2\sigma)=\mathbb P(6-2\sqrt6\le Y\le6+2\sqrt6)=\dfrac{66366}{175e^6}\approx0.940028[/tex]

Related Questions

Unfortunately, arsenic occurs naturally in some ground water†. a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. a well in texas is used to water cotton crops. this well is tested on a regular basis for arsenic. a random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. does this information indicate that the mean level of arsenic in this well is less than 8 ppb? use α = 0.01. (a) what is the level of significance? 0.01 state the null and alternate hypotheses. h0: μ = 8 ppb; h1: μ > 8 ppb h0: μ = 8 ppb; h1: μ < 8 ppb h0: μ > 8 ppb; h1: μ = 8 ppb h0: μ < 8 ppb; h1: μ = 8 ppb h0: μ = 8 ppb; h1: μ ≠ 8 ppb (b) what sampling distribution will you use? explain the rationale for your choice of sampling distribution. the standard normal, since the sample size is large and σ is known. the student's t, since the sample size is large and σ is unknown. the student's t, since the sample size is large and σ is known. the standard normal, since the sample size is large and σ is unknown. what is the value of the sample test statistic? (round your answer to three decimal places.) -2.483 (c) estimate the p-value. p-value > 0.250 0.125 < p-value < 0.250 0.050 < p-value < 0.125 0.025 < p-value < 0.050 0.005 < p-value < 0.025 p-value < 0.005 sketch the sampling distribution and show the area corresponding to the p-value. webassign plot webassign plot webassign plot webassign plot (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level α? at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Answers

Part A:

For a hypothesis test, the significant level is given by α. From the question, we were told that α = 0.01.

Therefore, the significant level is 0.01.

Our previous knowledge is that a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use, we know want to know from a sample of 36 tests whether the mean level of arsenic in a particular well is less than 8 ppb.

Therefore, the null and the alternative hypothesis are:

[tex]H_0:\mu=8\ pbb \\ \\ H_a:\mu\ \textless \ 8\ pbb[/tex]

Part B:

The sampling distribution to be used is the student's t, since the sample size is large and σ is unknown.

The test statistics is given by:

[tex]t= \frac{\bar{x}-\mu}{s/\sqrt{n}} \\ \\ = \frac{6.8-8}{2.9/\sqrt{36}} \\ \\ = \frac{-1.2}{2.9/6} = \frac{-1.2}{0.4833} \\ \\ =-2.483[/tex]

Part C:

The p-value for a t-distribution test statistics of -2.483 with a degree of freedom of 35 is given by 0.0090

Thus 0.005 < p-value < 0.025

Part D:

Since the p-value is less that the significant level, we reject the null hypothesis and conclude the data are statistically significant.

i.e.
at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

Part E:

Therefore, we conclude that there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Something greater tha 1/2 yard but less than 5/8 yard??

Answers

7/12. We know this because 7 is farther away from a whole.

Hope this helps!

Anything between 18 and 22.5 inches qualifies as a correct answer.

True or false, the decimal form of 3 3/8 is 3.38

Answers

False. The decimal form can be found by doing 3 + (3 ÷ 8). It would be 3.375.

Hope this helps!

For the box shown, the total area is 94 cm2. determine the value of x

Answers

Show the picture of the box

If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between x = 90 and x = 100 is p = 0.3085.
a. True
b. False

Answers

True can’t be sure though

Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.

Answers

Convert Ф = 90°, 45°, 0°, -45°, -90° into radans to obtain
Ф = π/2, π/4, 0, -π/4, -π/2 rad.

The given function is
v = 100 cos(ωt + Ф)

Create the following tables.
We shall use
ωt : 0 π/2 π (3/2)π 2π

Ф = π/2
ωt+Ф : π/2 π (3π)/2 2π (5π)/2
v : 0 -100 0 100 0

Ф = π/4
ωt+Ф : π/4 (3/4)π (5/4)π (7/4)π (9/4)π
v : 70.7 -70.7 -70.7 70.7 70.7

Ф = 0
ωt+Ф : 0 π/2 π (3/2)π 2π
v : 100 0 -100 0 100

Ф = -π/4
ωt+Ф : -π/4 π/4 (3/4)π (5/4)π (7/4)π
v : 70.7 70.7 -70.7 -70.7 70.7

Ф = -π/2
ωt+Ф: -π/2 0 π/2 π (3/2)π
v : 0 100 0 -100 0

Sketches of graphs for the different cases are shown below.

Explain how to solve 2x + 7 = 15

Answers

The x would be 4 because if you multiply 2 times 4, that's 8, and 8+7=15

You would work backwards:15-7=8, because you will be adding this anyways later, and then you see that 2x = 8, then divide both sides by two, and you are left with the equation: x = 4, and there is your answer. x = 4.

Its number 15. Thank you

Answers

Going from step 1 to step 2, the person has factored out x. However, this is incorrect because there is no x to factor from the last term d.

Factoring like this is simply the distributive property in reverse. We can check if we did the factoring right by distributing the outer term x back into the inner terms

Let's multiply the outer x by each of the inner terms (a, b and d)

x times a = ax
x times b = bx
x times d = dx <--- the result should be d and not dx

-----------------------------------------------------------------------------

Here is the proper way to solve for x. We first need to move the d over, which is done by subtracting d from both sides. Once all of the x terms are on one side, we can finally factor out the x. Then after that we divide both sides by the quantity (a+b)

k = ax + bx + d
k - d = ax + bx + d - d
k - d = ax + bx
k - d = x(a + b)
(k - d)/(a + b) = x(a + b)/(a + b)
(k - d)/(a + b) = x
x = (k - d)/(a + b)

The final answer is
x = (k - d)/(a + b)
which can be written as
[tex]x=\frac{k-d}{a+b}[/tex]
If you choose to use the first option, then make sure you use parenthesis as shown. The parenthesis are important to make sure that you divide all of "k-d" over all of "a+b" as one big fraction.

Why do you round 117290 up to 120000

Answers

because you round the 1 to the 7 and get 12 and everything that follows that number is 0.

bc its closest to that and not closest to 110000 or 10000

Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?

A-2/25

B-1/5

C-4/5

D-500/40

Answers

The correct answer would be A, 2/25.

Consider the equation y = 14 – 2x. with y on the vertical axis and x on the horizontal axis, the horizontal intercept of this line is

Answers

when y = 0, so 0 = 14 - 2x
2x = 14
x = 7
The horizontal intercept is (7,0)

Selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.6.

Answers

its 2.3 popluation its less than 2.6 and not less than 2.1

Find the specified element in the inverse of the given matrix

Answers

what is the given matrix?
you didn't show a matrix.
the components of the matrix are the elements.
and the elements of the inverse matrix are the elements of the inverse matrix
1)
so if matrix A is 1 4 1
2 5 2
3 6 3
2)
14114
25225
36336

3)
15 24 12
15 12 24
4)
[A]=(15+24+12=51)-(15+12+24=51)
[A]=0
5)
  52 23 25
63 23 36

41 11 14
63 33 36

41 12 14
52 12 25
6)

15-12 6-6 12-15

12-6 3-3 6-12

8-5   2-2 5-8

7)
3 0   -3

6 0 -6

3 0 -3
8)
(+)3 (-)0 (+)-3

(-)6 (+)0 (-)-6

(+)3 (-)0 (+)-3
=

  3 0 -3
-6 0   6
3 0 -3

9)
  3 -6 3
N= 0 0 0
-3 6 -3
10) the inverse of [A]= 1/|A|*[N]
which is in this case ⁻A= 0
because |A|=0

Lenny uses two pieces of yarn for a craft project. The first piece is 5.89 meters long. The second piece is 2.147 meters long. What is the total length of the two pieces of yarn? Enter your answer in the box. M__

Answers

5.89+2.147=8.037

The total length of the two pieces is 8.037 meters

Answer: 8.04 meters

Step-by-step explanation:

length of first piece of yarn = 5.89 meters

length of second piece of yarn = 2.147 meters

Total length of of the two pieces of yarn = length of first piece of yarn + length of second piece of yarn = 5.89 meters + 2.147 meters = 8.037 meters

The rule apply for the addition and subtraction is :

The least precise number present after the decimal point determines the number of significant figures in the answer.

Thus the answer will be 8.04 meters as least precise number 5.89 contains two decimal places.

Which pair of measurements is not equivalent?

24 feet, 8 yards
24 inches, 2 feet
10 feet, 120 inches
3 miles, 15,480 feet

Answers

The Answer Is D , 3 Miles Is 15840 Ft Not 15480 Ft
Hope This Helps

The pair of measurements that is not equivalent is 3 miles and 15,480 feet. All other pairs are equivalent when converted to the same units. This determines which measurements do not match in the same units.

To determine which pair of measurements is not equivalent, we need to convert them into the same units and compare them:

24 feet, 8 yards: 1 yard = 3 feet, so 8 yards = 8 * 3 = 24 feet. Therefore, 24 feet is equivalent to 8 yards.24 inches, 2 feet: 1 foot = 12 inches, so 2 feet = 2 * 12 = 24 inches. Therefore, 24 inches is equivalent to 2 feet.10 feet, 120 inches: 1 foot = 12 inches, so 120 inches = 120 / 12 = 10 feet. Therefore, 10 feet is equivalent to 120 inches.3 miles, 15,480 feet: 1 mile = 5280 feet, so 3 miles = 3 * 5280 = 15,840 feet. Therefore, 3 miles is not equivalent to 15,480 feet.

Thus, the pair of measurements that is not equivalent is 3 miles, 15,480 feet.

A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.

Answers

Hello!

34% of 39 is 13.26 ( 34% = .34 × 39 = 13.26)

Subtract that from 39 to find the amount of the discount:

39 - 13.26 = 25.74

So, the amount of discount on the backback is 25.74%.

^ And that's your answer! I hope this was helpful! :)

124,248-55,679 show me how you get this answer

Answers

124,248
- 55,679

68,569

Find the 75th derivative of y = cos(2x).

Answers

Given: y = cos(2x).

Let y⁽ⁿ⁾ denote the n-th derivative of y wrt x.

The first few derivatives of y wrt x are the following:
n=1: y⁽¹⁾ = - 2¹ sin(2x)
n=2: y⁽²⁾ = - 2² cos(2x)
n=3: y⁽³⁾ = + 2³ sin(2x)
n=4: y⁽⁴⁾ = + 2⁴ cos(2x)
n=5: y⁽⁵⁾ = - 2⁵ sin(2x)
and so on

A pattern emerges
y⁽ⁿ⁾ = - 2ⁿ sin(2x) for n = 1, 5, 9, ...,
= - 2ⁿ cos(2x) for n = 2, 6, 10, ...,
= + 2ⁿ sin(2x) for n = 3, 7, 11, ...,
= + 2ⁿ cos(2x) for n = 4, 8, 12, ....
For n=75, we seek a constant, a, which begins with 1,2,3, or 4 such that
a + 4(n-1) = 75
That is,
n = (75-a)/4 is an integer.
Try a = 1: n = 18.5 (reject)
a = 2: n = 18.25 (reject)
a = 3: n = 18 (accept)

Therefore, y⁽⁷⁵⁾ = + 2⁷⁵ sin(2x).

Answer: 2⁷⁵ sin(2x)

Final answer:

The 75th derivative of y = cos(2x) can be found by dividing 75 by 4 to find the cycle it falls into due to the repeating pattern of cos and sin. Due to remainder 3 after division, the 75th derivative is equivalent to the 3rd derivative from the cycle, which is 8sin(2x), but scaled by 2 to the power of the number of completed cycles (18). This gives the final answer 2^18 * 8sin(2x).

Explanation:

The process of finding the 75th derivative of a function can seem daunting or time-consuming, but with functions like cosines and sines, we can rely on the cycling pattern of these functions to simplify the task. This will significantly decrease the amount of computational effort needed.

When you find the derivative of y = cos(2x), the function cycles in a pattern every four times. The first derivative of y = cos(2x) is -2sin(2x), the second derivative is -4cos(2x), the third derivative is 8sin(2x), and the fourth derivative is 16cos(2x). As you can see, we've returned to the original function (scaled by a factor of 16).

So to find the 75th derivative, divide 75 by 4 to get remainder of 3. This means the 75th derivative is the same as the 3rd derivative, but scaled by 2 to the power of the number of full cycles (which is 18). Hence, the 75th derivative of y = cos(2x) is 2^18 * 8sin(2x).

Learn more about Derivatives of functions here:

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Suppose in a market for iTune cards demand is Qd = 1500 - 250P, and supply is Qs = 850P. Find the equilibrium P* and Q*.

Answers

At equilibrium point, the demand equation is equal to the supply equation.

Given that the demand is Qd = 1500 - 250P, and supply is Qs = 850P, at equilibrium,

1500 - 250P = 850P

850P + 250P = 1500

1,100P = 1,500

P = $1.36

and the equilibruim Q is 1500 - 250(1.36) = 1,159

Therefore, the equilibruim P* is $1.36 and the equilibruim Q* is 1,159.

A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250 pounds and it has uniform density. a = 15 and b = 39.

Answers

Answer:

(a) The density of flag is [tex]\dfrac{25}{27}[/tex] Pounds per square foot

(b) The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex] Pounds

(c) The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds

(d) The exact work by roof is 1250 foot-pounds

Step-by-step explanation:

(a) We are given a flag in the shape of a right triangle.

The total weight of flag is 250 pounds and Uniform density.

Base of the flag [tex]=\sqrt{b^2-a^2}[/tex]

[tex]=\sqrt{39^2-15^2}=36[/tex]

Area of the flag [tex]=\dfrac{1}{2}\times 36\times 15 = 270[/tex]

Weight of flag = 250 pounds

[tex]Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}[/tex]

Hence, The density of flag is [tex]\dfrac{25}{27}[/tex]

(b) Weight of strip which is h feet below the roof.

Length of strip [tex]=\dfrac{36}{15}(15-h)[/tex]

Width of strip [tex]\Delta h[/tex]

Weight = Density x area

[tex]=\dfrac{25}{27}\times \dfrac{36}{15}(15-h)[/tex]

[tex]=\dfrac{20}{9}(15-h)\Delta h[/tex]

Hence, The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex]

work[tex]=Weight\times displacement[/tex]

[tex]=\dfrac{20}{9}(15-h)\Delta h\times h[/tex]

[tex]=\dfrac{20}{9}(15-h)h\Delta h[/tex]

Hence, The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds

(d) Exact work on the roof by hanging flag

[tex]W=\int_0^{15}\dfrac{20}{9}(15-h)hd h[/tex]

[tex]W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}[/tex]

[tex]W=1250-0[/tex]

[tex]W=1250[/tex]

Hence, The exact work by roof is 1250 foot-pounds

Final answer:

The weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.

Explanation:

To find the centroid of a right triangle, we can use the following formulas:

[tex]\[ x_c = \frac{b}{3} \][/tex]

[tex]\[ y_c = \frac{a}{3} \][/tex]

Where:

[tex]- $ x_c $[/tex] is the x-coordinate of the centroid.

[tex]- $ y_c $[/tex] is the y-coordinate of the centroid.

[tex]- $ a $[/tex] is the length of the side perpendicular to the base (height).

[tex]- $ b $[/tex] is the length of the base.

Given $ a = 15 $ and $ b = 39 $, we can calculate the centroid as follows:

[tex]\[ x_c = \frac{39}{3} = 13 \][/tex]

[tex]\[ y_c = \frac{15}{3} = 5 \][/tex]

So, the centroid of the triangle is located at the point (13, 5).

Now, regarding the weight distribution, if the flag has uniform density, the center of mass (or centroid) would be the point where the total weight is concentrated. Since the total weight of the flag is 250 pounds, and the centroid is the point of concentration of mass, the entire weight of the flag, 250 pounds, can be considered to act at the centroid.

Therefore, the weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.

James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80

Answers

so James covers 8 meters in the first second....then he sprints 9 meters per second......
9 seconds after the race....so there are 8 seconds that he is sprinting 9 meters per second.....(8 * 9) = 72 meters....plus the 8 meters for the 1st second = (72 + 8) = 80 meters....
and if it is 100 meter race, and he has ran 80 meters, then that leaves 20 meters from the finish line....answer is D

Answer:

Option b. 20 meters

Step-by-step explanation:

James covers a distance of 8 meters in the first second of 100 meter race.

Then, he sprints at a speed of 9 meters per second.

We have to find how far is James from the finish line 9 seconds after the start of the race.

James covers distance in first second = 8 meters.

Time remaining in 9 seconds after running 8 meter = 9 - 1 = 8 seconds.

In another 8 seconds James covers the distance = speed × time

= 9 × 8 = 72 meters

Total distance covered in 9 seconds = 8 + 72 = 80 meters

Distance remaining in 100 meter race after 9 seconds = 100 - 80 = 20 meters.

James is 20 meters far from the finish line 9 seconds after the race has started.

Option b. 20 meters is the answer.

I an a factor of 28. the other factor is 4. what number am i

Answers

Hello there!

The correct answer is 7

Because 7 * 4 = 28

I hope this helps!

7 because 7*4=28
Hope this helps have a nice nite

In a 4 x 3 factorial design, there are how many levels of the first grouping factor?

Answers

there are 4 levels in the first grouping factor

List any restrictions on the domain for the equation [tex] \frac{x+9}{x+2} [/tex]

Answers

for a fraction, if the denominator turns to 0, the fraction becomes undefined, and therefore, that's a restriction on a rational.

now, what values of "x" makes the denominator 0? let's check,

x+2 = 0

x = -2

so, if "x" ever becomes -2, then you'd get

[tex]\bf \cfrac{x+9}{x+2}\implies \cfrac{x+9}{-2+2}\implies \implies \cfrac{-2+9}{-2+2}\implies \stackrel{und efined}{\cfrac{7}{0}}[/tex]

so, the domain, or values "x" can take on safely, are any real numbers EXCEPT -2.

Please help badly I cannot answer

Answers

so, you asked 356 folks if they like drawing, 89 say they do.

now, if we take 356 as the 100%, what is 89 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 356&100\\ 89&x \end{array}\implies \cfrac{356}{89}=\cfrac{100}{x}\implies x=\cfrac{89\cdot 100}{356}[/tex]

Write an equation of the line in the figure.

Answers

the slope is 6/5 and the y intercept is -1
Slope intercept y = 6/5x -1
Point slope form (y - 5) = 6/5 (x - 5)

find the product. List the units. 8 h $9/h

Answers

8h = 8(9) = 72
answer
$72

The product is equivalent to $72.

What is a expression? What is a mathematical equation? What is Equation Modelling?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a rate of $9 per hour for 8 hours.

Now, for 1 hour, the cost is $9. Therefore, for 8 hours, we can write -

x = 9 x 8

x = $72

Therefore, the product is equivalent to $72.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

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Nancy withdrew $19 from her bank account to pay for markers write in integer to represent this situation

Answers

Hello!

Withdrawing is like taking out money from her account.

So, the integer that represents this situation is -$19.

I hope that was helpful! c:

Multiply 29 and 0.85 to get $24.65

Then, subtract 29- 24.65

Final answer: $4.35

5x-3 (2x-4)=7x+16. solve for x

Answers

5x-3(2x-4)=7x+16
1st step: Distributive Property
5x-6x+12=7x+16
2nd step: Combine Like Terms
-x+12=7x+16
-12 . -12
-x=7x+4
-7x -7x
-8x=4
/-8 . /-8
x=-1/2

The temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours.
Explain why the average temperature change was –5ºF per hour.

Answers

It changes every 1 5 degrees because 10 divided by 5 is 2

I hope this helped ya :)

The temperature fall can be represented by −10. To find the average change per hour, divide −10 by 2. −10 divided by 2 is −5.

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