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
WHAT THREE EQUAL NUMBERS COULD YOU ADD TO GET 180
VARVARA [1.3K]
60 60 and 60. Hope I helped!
3 0
3 years ago
Read 2 more answers
What is the ninth term in the binomial expansion of (x – 2y)13? 329,472x5y8 –329,472x5y8 –41,184x8y5 41,184x8y5
scZoUnD [109]
Hello,
Please, see the detailed solution in the attached file.
Thanks.

4 0
3 years ago
In the diagram below of regular pentagon ABCDE,<br> EB is drawn.<br><br> What is the measure of AEB?
Drupady [299]

Answer:

36°

Step-by-step explanation:

< EAB = 180 - (360/5) = 180-72=108°

so, < AEB = (180-108)/2 = 72/2 = 36°

6 0
3 years ago
Determine the slope of each side of the polygon
Pavlova-9 [17]
W- (3,4)
Z- (-1,1)
X-(-1,-3)
Y-(-4,1)
7 0
3 years ago
Read 2 more answers
NEED HELP! DUE TOMORROW 2/4/2021
m_a_m_a [10]
The second Version of the game is greater for hitting the down button because substituting any number for x, the second equation would always end up having a greater amount.
6 0
3 years ago
Other questions:
  • The diagram below shows a set of three different sized containers tanner used for storing dry goods. The largest container held
    9·2 answers
  • What is the value of r? 1.9r+0.1r=0.6 Enter your answer as a decimal in the box. r =
    8·1 answer
  • Amber spent 1,793.34 on a TV after an 18% discount and on an 8% tax. What was the original price of the TV?
    6·1 answer
  • PLEASE HELP ASAPPPPPPPP
    5·2 answers
  • Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • Destiny is making a gelatin dessert for a party. She plans
    6·1 answer
  • Which of the following sentences is true? Use the number line to help you decide.
    5·1 answer
  • What fraction is equivalent to. —-<br> 0.45?
    6·2 answers
  • Pls help will mark brainliest
    15·1 answer
  • Find the area of the figure shown
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!