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
andre [41]
3 years ago
10

Suppose that, after measuring the duration of many telephone calls, a telephone company found their data was well-approximated b

y the density function p(x) = 0.1 e^-0.1x, where x is the duration of a call, in minutes. What percentage of calls last between 2 and 3 minutes? Percent = percent What percentage of calls last 2 minutes or less? Percent = percent What percentage of calls last 4 minutes or more? Percent = percent What is the cumulative distribution function, P(t)? P(t) =
Mathematics
1 answer:
Musya8 [376]3 years ago
6 0

Answer:

a) 7.79%

b) 67.03%

c) Cumulative Distribution Function

P(t) = \displaystyle\int^{\infty}_{-\infty} 0.1e^{-0.1t}~dt\\\\= \displaystyle\int^{b}_{a} 0.1e^{-0.1t}~dt, ~~a\leq t \leq b

Step-by-step explanation:

We are given the following in the question:

p(x) = 0.1 e^{-0.1x}

where x is the duration of a call, in minutes.

a) P( calls last between 2 and 3 minutes)

=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%

b) P(calls last 4 minutes or more)

=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%

c) cumulative distribution function

P(t) = \displaystyle\int^{\infty}_{-\infty} 0.1e^{-0.1t}~dt\\\\= \displaystyle\int^{b}_{a} 0.1e^{-0.1t}~dt, ~~a\leq t \leq b

You might be interested in
In 12 hours, how many more kilometers could the yellow car go than the red car? show your work
trasher [3.6K]

Answer:

144

Step-by-step explanation:

12 times 12

3 0
3 years ago
A person can pay $27 for a membership to the science Museum and then go to the museum for just a $1.00 per visit. What is the ma
HACTEHA [7]

Answer:

10

Step-by-step explanation:

27 + 1(10) = 37

7 0
3 years ago
Read 2 more answers
Find the 10th term of the following geometric sequence: 2, 8, 32, 128.        A. 164,357   B. 621,325   C. 524,288   D. 248,221
Galina-37 [17]
Common ratio = 8/2 = 32/8 = 4

10th term  = a1*r^(n - 1)   where a1 = 2 , r = 4 and n = 10
                = 2 * 4^9
                =  524,288
4 0
3 years ago
Read 2 more answers
How do I do this problem <br> -6(x+1)-18=26+4
pogonyaev

Answer:

x=-9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−6(x+1)−18=26+4

(−6)(x)+(−6)(1)+−18=26+4(Distribute)

−6x+−6+−18=26+4

(−6x)+(−6+−18)=(26+4)(Combine Like Terms)

−6x+−24=30

−6x−24=30

Step 2: Add 24 to both sides.

−6x−24+24=30+24

−6x=54

Step 3: Divide both sides by -6.

−6x

−6

=

54

−6

x=−9

Answer:

x=−9

5 0
3 years ago
HELP PLEASE!! | A box of granola bars that costs $4.00 is on sale for “buy 2, get 1 free.” What is the true percent of discount
Dafna11 [192]

Answer:

75%

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • A triangle drawn on a map has sides that measure 15 cm, 8 cm, and 10 cm. The shortest of the corresponding real-life distances i
    10·1 answer
  • What is the perimeter, P, of a rectangle that has a length of x + 8 and a width of y − 1?
    15·2 answers
  • Good at area pls helppp <br><br> Find the area. The figure is not drawn to scale.
    5·1 answer
  • A snack bar sells two sizes of snack packs. A large snack pack costs 5 dollars. A small snack pack costs 3 dollars. In one day t
    10·1 answer
  • 1cm represents 5.4miles on a scale drawing, what distance does 17.1cm on the scale drawing represent in real life.
    13·1 answer
  • Hi
    5·1 answer
  • Which of the following equations has the steepest slope?
    7·1 answer
  • Let g(x)=Intragal from 0 to x f(t) dt, where r is the function whos graph is shown.
    5·1 answer
  • Find the length of BC.
    11·1 answer
  • A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8).
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!