Suppose X has an exponential distribution with lambda equals 5. Determine the following. Round the answers to 3 decimal places.a) Upper P left-parenthesis Upper X less-than-or-equal-to 0 right-parenthesis equalsb) Upper P left-parenthesis Upper X greater-than-or-equal-to 2 right-parenthesis equalsc) Upper P left-parenthesis Upper X less-than-or-equal-to 1 right-parenthesis equalsd) Upper P left-parenthesis 1 less-than Upper X less-than 2 right-parenthesis equalse) Find the value of x such that Upper P left-parenthesis Upper X less-than x right-parenthesis equals 0.05.

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

The random variable X follows an exponential distribution with λ = 5.

The probability density function of X is:

[tex]f_{X}(x)=\lambda\cdot e^{-\lambda\cdot x};\ 0<x<\infty[/tex]

[tex]P(X\leq x)=1-e^{-\lambda\cdot x}\\\\P(X\geq x)=e^{-\lambda\cdot x}[/tex]

(a)

Compute the value of P (X ≤ 0) as follows:

[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]

               [tex]=1-e^{-5\times 0}\\\\=1-1\\\\=0[/tex]

Thus, the value of P (X ≤ 0) is 0.

(b)

Compute the value of P (X ≥ 2) as follows:

[tex]P(X\geq 2)=e^{-5\times 2}=4.54\times 10^{-5}\approx 0[/tex]

Thus, the value of P (X ≥ 2) is approximately 0.

(c)

Compute the value of P (X ≤ 1) as follows:

[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]

               [tex]=1-e^{-5\times 1}\\\\=1-0.00674\\\\=0.99326[/tex]

Thus, the value of P (X ≤ 1) is 0.99326.

(d)

Compute the value of P (1 ≤ X ≤ 2) as follows:

[tex]P(1<X<2)=\int\limits^{2}_{1} {5\times e^{-5x}} \, dx \\\\=5\times [\frac{e^{-5x}}{-5}]^{2}_{1} \\\\=5\times [\frac{0-0.00674}{-5}]\\\\=0.0067[/tex]

Thus, the value of P (1 ≤ X ≤ 2) is 0.0067.

(e)

Compute the value of x such that P (X < x) = 0.05 as follows:

[tex]P(X<x)=0.05\\\\\int\limits^{x}_{0} {5\times e^{-5x}} \, dx =0.05\\\\5\times [\frac{e^{-5x}}{-5}]^{x}_{0} =0.05\\\\1-e^{-5x}=0.05\\\\-e^{-5x}=0.95\\\\-5x=\ln(0.95)\\\\-5x=-0.05\\\\x=0.01\\\\[/tex]

Thus, the value of x is 0.01.


Related Questions

how does the graph below change between point A and point B?​

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I am not able to solve this because there is no graph shown.

how do you take the square root of a perfect square variable​

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Search Results
Featured snippet from the web
Answer: “Just take the number and multiply it by itself! If you square an integer, you get a perfect square!”

Of the 50 students in mr motchells classes 60% are girls on friday 20% of the girls in the classes wore jeans how mnay girls wore jeans

Answers

Answer:it would be 20

Step-by-step explanation:

Answer: 20.

Step-by-step explanation: 60% of 50 is 30 (students). 20% of it would be 20 (students).

Order the following numbers from least to greatest. Put the lowest number on the left. 50 25 0 -75​

Answers

Answer:

-75 0 25 50

Step-by-step explanation:

the order it needs to be in is -75,0,25,50

Which of the following statements about developing a personal fitness program is NOT true?
A. When developing a personal fitness program, it is important to implement strategies that will help
maintain the program as well as give it a successful start.
B. Personal factors such as age, health concerns, and likes are important to consider when
developing a personal fitness program.
C. The starting skill level of the physical activities included in a personal fitness program should be
determined from other individuals' fitness programs.
D. The FITT principle should be used when developing a personal fitness program.

Answers

Answer:

C.

Step-by-step explanation:

The surface area of a sphere with a diameter of 12 units is:

Answers

Answer:

452.39

Step-by-step explanation:

Using the formula

A=4pi r ^2

D=2r

A=pie r d^2

= pi. 12^2

=452.39

Use base ten blocks or an area model to find the product. 2.1 x 1.5

Answers

It’s 3.15... I hope it helps!!! Have an amazing day love

10 yd
4 yd
What is the area of the shaded portion to the nearest hundredth? Enter the answer in the box.
square yards

What is the answer of the green portion?

Answers

Answer : The area of the shaded portion is 33.72 yd².

Step-by-step explanation :

Given:

Length of the box = 10 yd

Width of the box = 4 yd

Area of the shaded portion = Area of rectangular box - Area of half circle

First we have to calculate the area of rectangular box.

Area of rectangular box = Length of the box × Width of the box

Area of rectangular box = 10 yd × 4 yd

Area of rectangular box = 40 yd²

Now we have to calculate the area of half circle.

As we know that:

Area of circle = π × r²

where,

r = radius of circle

Area of half circle = [tex]\frac{\pi \times r^2}{2}[/tex]

Radius of circle = [tex]\frac{4yd}{2}=2yd[/tex]

Area of half circle = [tex]\frac{3.14 \times (2yd)^2}{2}[/tex]

Area of half circle = 6.28 yd²

Now we have to calculate the area of the shaded portion.

Area of the shaded portion = Area of rectangular box - Area of half circle

Area of the shaded portion =  40 yd² - 6.28 yd²

Area of the shaded portion =  33.72 yd²

Therefore, the area of the shaded portion is 33.72 yd².

the set of letters in the word mathematics is finite?​

Answers

Answer:

Yes

Step-by-step explanation:

Find all integer solutions to the equation 91x + 329y = 49.

Answers

Answer:

dont waste points get wolfframAlpha

Vaughn paints his porch floor and also the porch floors of 9 neighbors. Each floor is a rectangle that is 8.4 feet long and 6.9 feet wide.

Answers

Answer:

579.6 ft²

Step-by-step explanation:

10(8.4×6.9)

Answer:

521.64

Step-by-step explanation:

first you do 8.4 times 6.9 which gets you 57.96 and then you multiply that my 9 which gets you 521.64.

What is this simplified step by step

Answers

I say it’s 28 because I used a calculator sooo this was easy so yeah the answer is 28

Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)

Answers

Answer:

x-intercept: (-40, 0)

y-intercept: (0, 15)

Step-by-step explanation:

The x-intercept is the value of x when y = 0. By looking at the graph, you can tell when y = 0, x = - 40. The x-intercept is the point that crosses the x-axis.

The y-intercept is the value of y when x = 0. By looking at the graph, you can tell y = 15 when x =0. The y-intercept is the point that crosses the y-axis.

when your cousin was born, she was 21 4/5 inches long. when your friends was born he was 21 3/4 inches long. who was longer at birth? how much longer?​

Answers

Answer:

cousin

1/20 inches

Step-by-step explanation:

Hi there !

cousin

21 4/5 = (21×5+4)/5 = 109/5

friend

21 3/4 = (21×4+3)/4 = 78/4

lcm(4 ; 5) = 20

⁴⁾109/5 = 436/20 (cousin)

⁵⁾87/4 = 435/20 (friend)

436/20 > 435/20

cousin > friend

436/20 - 435/20 = 1/20 inches longer (cousin)

Good luck !

In the year 2004, a survey was undertaken to find whether citizens of a certain political party supported their party's candidate for governor. In a sample of 300 citizens of this party, 95% of them expressed support for their party's candidate. A similar survey was conducted four years later and showed that 91% of a sample of 350 citizens of this party expressed support for their party's candidate. Construct a 95% confidence interval for the difference in population proportions of citizens of this party who supported their gubernatorial candidate in 2004 and citizens of this party who supported their gubernatorial candidate four years later. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.) z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

Answers

Answer:

The 95% confidence interval for the difference in population proportions is (0.001, 0.079).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference in population proportions is:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

The information provided is as follows:

[tex]\hat p_{1}=0.95\\\hat p_{2}=0.91\\n_{1}=300\\n_{2}=350\\[/tex]

The critical value of z for 95% confidence level is 1.96.

Compute the 95% confidence interval for the difference in population proportions as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

     [tex]=(0.95-0.91)\pm 1.96\times\sqrt{\frac{0.95(1-0.95)}{300}+\frac{0.91(1-0.91)}{350}}\\\\=0.04\pm 0.0388\\\\=(0.0012, 0.0788)\\\\\approx (0.001, 0.079)[/tex]

Thus, the 95% confidence interval for the difference in population proportions is (0.001, 0.079).

Fill in the value which would complete the square:
X^2 + 10x +____

Answers

Answer:

25

Step-by-step explanation:

(x+5)(x+5)=x(x+5)5(x+5)

=x^2+5x+5x+25

=x^2+10x+25

i hope it is clear

Simplify the following equation. 4x + 2 = 8x - 5

Answers

Answer:

1.75= X

Step-by-step explanation:

4x+2=8x-5

-4x     -4x

2=4x-5

+5      +5

7=4x

divide by 4

1.75=x

Mark brainilst plzzz

Madison's checking account had a balance of - $45. Then she wrote a check to pay her utility bill for $34. Write an expression to represent Madison's situation.

Answers

-$45 - 34 = -79 explain when you subtract a negative to a positive you come out with a negative

Point J is between H and K on line segment HK. Use the given information to solve for X. Also find the length of line segment HJ.
HK = 33
HJ = 3x-4
JK = 2x+7
X= ?
The length of line segment HJ= ?

Answers

Answer:

x=-3, so now u plug it in, 3(-3)-4=?

answer: HJ is -13.

Using line segments concepts, it is found that:

The value of x is 6.The length of line segment HJ is 14.

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

Point J is between H and K in a line segment HK, thus:

[tex]HK = HJ + JK[/tex]

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

We are given that:

[tex]HK = 33[/tex][tex]HJ = 3x - 4[/tex][tex]JK = 2x + 7[/tex]

Thus, replacing into the equation, it is possible to solve for x.

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

[tex]HK = HJ + JK[/tex]

[tex]33 = 3x - 4 + 2x + 7[/tex]

[tex]5x + 3 = 33[/tex]

[tex]5x = 30[/tex]

[tex]x = \frac{30}{5}[/tex]

[tex]x = 6[/tex]

The value of x is 6.

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

The length of line segment HJ is:

[tex]HJ = 3x - 4 = 3(6) - 4 = 18 - 4 = 14[/tex]

A similar problem is given at https://brainly.com/question/24476050

The number of feet it takes for a car traveling at x miles per hour to stop on dry, level concrete is given by the polynomial 0.06x2+1.1x. Find the stopping distance, in feet, when x=40 miles per hour.

Answers

Answer:

The answer is 140

Step-by-step explanation:

We are asked to find the stopping distance, in feet, when x=40 miles per hour. We will substitute this into the polynomial expression 0.06x2+1.1x, and then simplify using the order of operations.

0.06(40)2+1.1(40)=96+44=140

When driving at x=40 miles per hour, the stopping distance is 140ft.

what is the solution for the following equation? 3(a-7)=14-4a​

Answers

Answer:

a= 5

Step-by-step explanation:

3 (a-7)= 14-4a -Remove Parentheses

3a-21=14-4a -Move the terms

3a+4a=14+21 -Collect like terms

7a=35 -Divide both sides

a=5 - Solution

what is 3 + 2x = -6x + 4​

Answers

Answer:

x = 1/8

Step-by-step explanation:

Hahaha A little help? Plss

Answers

Answer:

Step-by-step explanation:

6/58=3/29

Answer:

3/29

Step-by-step explanation:

Write the equation in slope intercept form. -4x + 4y = 16

Answers

Answer:

y = x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

- 4x + 4y = 16 ( add 4x to both sides )

4y = 4x + 16 ( divide all terms by 4 )

y = x + 4 ← in slope- intercept form

what is -3(2u-3w-4)

please answerr

Answers

Answer:

-6u +9 w +12

Step-by-step explanation:

The answer is 6c—9w—12

Please I need some answers one or two are fine

Answers

Answer:

A. 10,000

B. 1,000,000

C. 10,000,000,000

D. 1,000,000,000,000

Step-by-step explanation:

10,000/ 10∧4 = 1

1,000,000/ 10∧6 = 1

10,000,000,000/ 10∧10 = 1

1,000,000,000,000/ 10∧12 = 1

Hope this helps! Good luck!

QUESTION 1 Let’s say that an investigator is interested in the effects of caring for a person with ALS (Lou Gehrig’s disease) on physical and mental health. In particular, the researcher wants to know whether ALS caregivers suffer from clinically elevated levels of depression. They administer the Beck Depression Inventory (BDI) to 20 ALS caregivers. Scores on the BDI range from zero to 40. Scores at or above 25 are considered to reflect clinically significant levels of depression. The mean depression score for the 20 caregivers in the sample is 28. The standard deviation for this sample is 3.0. Do these data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25? This example is not a perfect example of a "true experiment," so the independent and dependent variable are not as clearly identifiable as some other examples. In this example, what is the dependent/outcome variable? Beck Depression Inventory scores How many ALS caregivers there are in the study Whether the caregivers are taking care of someone who has ALS vs. cancer The ALS caregivers vs. the national norms for adults

Answers

Answer:

The decision rule is

Reject the null hypothesis

The conclusion is  

There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25

dependent/outcome variable

Generally the dependent variable is  Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers

Step-by-step explanation:

From the question we are told that

  The sample size is  n = 20

  The population mean is  [tex]\mu  =  25[/tex]

   The sample mean is  [tex]\= x  = 28[/tex]

  The standard deviation is  [tex] s  =  3.0[/tex]

  The null hypothesis is [tex]H_o  :  \mu  =  25[/tex]

  The alternative hypothesis is  [tex]H_a  :  \mu  >  25[/tex]

  Generally the test statistics is mathematically represented as

     [tex]z = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]

=>  [tex]z= \frac{ 28 -25 }{ \frac{3.0}{\sqrt{20 } } }[/tex]

=>  [tex]z=  4.47[/tex]

 Generally the probability of  z from the z- table is

   [tex]p-value  =  P(Z >  4.47) =  0.000[/tex]

From the values obtained we see that  [tex]p-value  <  \alpha[/tex] hence

The decision rule is

Reject the null hypothesis

The conclusion is  

There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25

Generally the dependent variable is  Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers

A small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in one hour? (50 minutes = 56 hour)

Answers

Answer:

124.8 miles

Step-by-step explanation:

104 divided by 5 equals 20.8, then 20.8 times 6 equals 124.8

is it A B C D Pls tell me ​

Answers

20 is 1000 times of 0.02. Correct answer is option C.

What is Decimal ?

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, given value

0.02 = 002/100

        = 2/100

On multiply numerator and denominator by 10, we get

0.02 = 20/1000

or 20 = 1000 X 0.02

Thus, 20 is 1000 times of 0.02.

Learn more about Decimal Number from:

https://brainly.com/question/4708407

#SPJ1

(30 points!)
determine which lines are parallel??​

Answers

Answer:

looks like the parallel lines are "l" and "n"

Step-by-step explanation:

when two lines are parallel, they should be across from each other going the same way. For example: / / , or \ \  sometimes even on top of each other. It can't be line "m" because it seems a little slanted. Parallel lines have to be the same length and same size. It can't be line "t" because the line is going in a different direction.

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