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
Please help fast for 10 points and bro list!! And it’s multiple choice!!! ANSWER ONLY IF YOU KNOW!! PLEASE EXPLAIN PREFER AND EX
xxTIMURxx [149]

Answer:

D (x-10)

Step-by-step explanation:

x^2 - 8x - 20

(x -10)(x+2)

7 0
2 years ago
Mary can read 10 pages in 20 minutes how fast can she read
Zanzabum

Answer:

Mary can read one page per two minutes.

Step-by-step explanation:

20 divided by 10 equals two

4 0
3 years ago
Read 2 more answers
Which ofnthe following shows the correct use of distributive property when solving 1/3(33-x)=135,2
madam [21]

Answer: OPTION C.

Step-by-step explanation:

The missing options are:

A. (33 - x) = \frac{1}{3} * 135.2\\\\B. (\frac{1}{3} *33) - \frac{1}{3} x = \frac{1}{3} * 135.2\\\\C.(\frac{1}{3}  * 33) - \frac{1}{3} x = 135.2\\\\D. (\frac{1}{3}  * 33) + \frac{1}{3} x = 135.2

In order to solve this exercise you need to remember the following:

1. The Distributive property states that:

a(b+c)=ab+ac\\\\a(b-c)=ab-ac

2. The multiplication of signs:

(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-

In this case the exercise gives you the following equation:

\frac{1}{3}(33-x)=135.2

Since you need to solve for the variable "x" in order to  find its value, the first  step you must apply in the in the procedure is to eliminate the parentheses applying the Distributive property.

Then, you must multiply everyting inside the parentheses by \frac{1}{3}.

Therefore,based on the explanation, you know that the correct use of the Distributive property is:

\frac{1}{3}*33-\frac{1}{3}x=135.2

8 0
3 years ago
Find the distance between the two points rounding to the nearest tenth (if necessary).
Levart [38]

Answer:

The answer is 13

5 0
2 years ago
Read 2 more answers
The measure of angle is<br> _________ degrees.
Gnesinka [82]

Answer:

65 degrees

Step-by-step explanation:

Triangle = 180 degrees

Straight line = 180 degrees

180 - 145 = 35

35 + 80 = 115

180 - 115 = 65 degrees

7 0
3 years ago
Other questions:
  • A man bought a bicycle for $400 and sold it at a loss of 35%. How much did he lose?
    14·2 answers
  • The measures of the three angles are 45°, 75°, and 60°. how many triangles can you make
    7·1 answer
  • Evaluate the expression 12-(8+3)
    11·2 answers
  • 11, 16, 12, 7, 23, 9, 5, 5 What is the median of the data?
    8·2 answers
  • Which of the lines graphed has a slope of -1/2 and a y-intercept of 3
    13·1 answer
  • ON A BUS ROUTE, THREE NEW PEOPLE GET ON THE BUS AT EACH STOP AFTER THE FIRST ONE. AT THE FIRST STOP SEVEN PEOPLE GET ON THE BUS.
    5·1 answer
  • What is the equation of the line that passes through the point (8, 8) and has a<br> slope of -22
    12·1 answer
  • Can someone help me please!!
    14·2 answers
  • 5.6 x 5.6 x 6.16 x 6.16
    13·1 answer
  • How can you simplify integer expressions that contain more than one operation?<br> answer quick pls
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!