1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
n200080 [17]
2 years ago
15

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

> 1. Determine the following (round all of your answers to 3 decimal places):
a) P(x < 5)=

b) P(x > 8)=

c) P(6 < x < 10)=

d) P(x < 6 or x > 10)=

3) Determine x such that P(X < x) = 0.75
Mathematics
1 answer:
natulia [17]2 years ago
8 0

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

       P(a < X < b) =  \int_{a}^{b} \frac{2}{x^{3}} dx = 2\int_{a}^{b} x^{-3} dx

                            = 2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx    { Because \int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a }

                            = 2[ \frac{x^{-2} }{-2}]^{b}_a = \frac{2}{-2} [ x^{-2} ]^{b}_a

                            = -1 [ b^{-2} - a^{-2}  ] = \frac{1}{a^{2} } - \frac{1}{b^{2} }

a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }

     Comparing with general probability we get,

     P(1 < X < 5) = \frac{1}{1^{2} } - \frac{1}{5^{2} } = 1 - \frac{1}{25} = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/8^{2} - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = \frac{1}{6^{2} } - \frac{1}{10^{2} } = \frac{1}{36} - \frac{1}{100 } = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

                                = (\frac{1}{1^{2} } - \frac{1}{6^{2} }) + (1/10^{2} - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

               ⇒  P(1 < X < x) = 0.75

               ⇒  \frac{1}{1^{2} } - \frac{1}{x^{2} } = 0.75

               ⇒  \frac{1} {x^{2} } = 1 - 0.75 = 0.25

               ⇒  x^{2} = \frac{1}{0.25}   ⇒ x^{2} = 4 ⇒ x = 2  

Therefore, value of x such that P(X < x) = 0.75 is 2.

You might be interested in
Can I get help on this one
ivann1987 [24]

Answer:

150

Step-by-step explanation:

The angle as a whole is 180 degrees. 150 and 30 are supplementary angles because they add up to equal 180.

5 0
3 years ago
-1/2 (-6x + 3) plz helpppp
umka21 [38]

Answer:

-1/2

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Which expression has the same value as 15+24
lakkis [162]
15+24= put it in the calculator u will find the answer(hope this helped)
6 0
3 years ago
Read 2 more answers
What is 1+1=<br> The answer, please for my 1-YEAR-OLD sister that doesn't understand...anything
inessss [21]

Answer:

The answer is 2

Step-by-step explanation:

1+1=2

She can put 2 fingers up and count 1,2

5 0
3 years ago
ASAP!!! ILL GIVE BRAINLIEST !
Alex17521 [72]

Answer:

1) 60

2) 60

3) 119

4) 59

Step-by-step explanation:

All triangle angles add up to 180 degrees. All lines with transversals add to 180 degrees. Use these rules and the measurements given to solve.

3 0
2 years ago
Other questions:
  • A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain245 ounces of a mixture
    10·1 answer
  • Anyone really good at stats?
    11·1 answer
  • How many even positive integers less than 300 can be written using the number 2 4 5 and 8?
    12·1 answer
  • Clare mixes 2 1/2 cups water with 1/3 cup orange juice conc. Hannmixes 1 2/3 cups water with 1/4 cup orange juice Conc. Which is
    14·1 answer
  • Solve for x <br><br>3(x-2)=9<br><br>answers <br><br>5<br><br>4<br><br>-5<br><br>-4​
    6·2 answers
  • Do the ratios 3 8 and 4 7 form a proportion?
    7·1 answer
  • When compared with the independent variable, how many of the graphs represent a linear relationship?
    9·1 answer
  • ABC was dilated to create A'B'C' (please help)
    14·1 answer
  • Pls help!!!! Urgent pls answer 19-36
    10·2 answers
  • 5.a.A tourist buys 5 pieces of Nepali cap at Rs 452 per piece including 13% VAT. How much will he recive while leaving Nepal?​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!