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
Alecsey [184]
3 years ago
7

Suppose X has an exponential distribution with mean equal to 23. Determine the following:

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

Answer:

a) P(X > 10) = 0.6473

b) P(X > 20) = 0.4190

c) P(X < 30) = 0.7288

d) x = 68.87

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

Mean equal to 23.

This means that m = 23, \mu = \frac{1}{23} = 0.0435

(a) P(X >10)

P(X > 10) = e^{-0.0435*10} = 0.6473

So

P(X > 10) = 0.6473

(b) P(X >20)

P(X > 20) = e^{-0.0435*20} = 0.4190

So

P(X > 20) = 0.4190

(c) P(X <30)

P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288

So

P(X < 30) = 0.7288

(d) Find the value of x such that P(X > x) = 0.05

So

P(X > x) = e^{-\mu x}

0.05 = e^{-0.0435x}

\ln{e^{-0.0435x}} = \ln{0.05}

-0.0435x = \ln{0.05}

x = -\frac{\ln{0.05}}{0.0435}

x = 68.87

You might be interested in
Jack invests $4200 in a savings account paying 5.25% compounded quarterly, how much is in the account after 30 months?
vova2212 [387]
It will have 25,000 dollars in 30 months
3 0
3 years ago
Peter uses unit cubes to build a figure in the shape of the letter X what is the fewest unit cubes that Peter can use to build t
lozanna [386]
I am not sure I am right but I think it depends on the size of the X.

4 0
3 years ago
Suppose z = cos 2 pie over 3 plus i sine 2 pie over 3, what is z to the fourth
ladessa [460]

Answer:

i have eaten apple pie but not this *cos pie

Step-by-step explanation:

is it tasty !! can you send recipie

4 0
2 years ago
Samir has written 10 pages
olganol [36]

Answer

85 pages in 5 months

Step-by-step explanation:

10+(15x5)=85

4 0
3 years ago
Read 2 more answers
Ashely is making $500 a week at her job. She receives a 20% pay raise. A year later she takes a 5% pay cut. How much money does
zheka24 [161]

Answer:

<em>$570 a week</em>

Step-by-step explanation:

<u>Percentage Calculations </u>

One tricky fact about percentages is that they are usually performed over the last computed quantity. It makes them non-additive. For example, a raise of 10% followed by a 10% some time later, is NOT a 20% of total raise

The question states Ashely is making $500 a week at her job and that she receives a 20% pay raise. After that raise she will make

\$500*(1+20/100)=\$500(1.2)=\$600 \text{ a week}

A year later she takes a 5% pay cut. We must be careful to take that percentage from the last earnings. She now makes

\$600(1-5/100)=\$600(0.95)=\$570\ a\ week

3 0
3 years ago
Other questions:
  • Which correctly gives the location of the point (7, –13)? A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV
    7·1 answer
  • What is 5% of 3,000?
    5·2 answers
  • 17x - 6 + 3x - 5 = x + 11 + 4x
    14·1 answer
  • PLZ ANSWER!! List all positive three-digit multiples of 99.
    9·1 answer
  • WRITE INEQUALITY'S FOR THE FOLLOWING SITUATIONS
    12·1 answer
  • In the figure AB = BC = CD = DA 2 3.2 units. The slope of AB is. What else do
    7·1 answer
  • Which expression is equivalent to 2(u+4)?<br> 2u+8<br> 8u+2<br> 8u<br> 6u
    12·1 answer
  • Please help I will give brainiest
    9·2 answers
  • Juan is participating in a 4 -day cross-country biking challenge. He biked for 61, 70, and 59 miles on the first three days. How
    7·1 answer
  • 2. Tristan wants to go bowling. He wants to spend no more than $25. It costs $3.00 to rent shoes and $4.50 for each game. What i
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!