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
trasher [3.6K]
3 years ago
14

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with mean 1/0.41/0

.4. What is (a) the probability that a repair time exceeds 33 hours? (b) the conditional probability that a repair takes at least 1010 hours, given that it takes more than 99 hours?
Mathematics
1 answer:
lbvjy [14]3 years ago
6 0

Answer:

a) P(t>3)=0.30

b) P(t>10|t>9)=0.67

Step-by-step explanation:

We have a repair time modeled as an exponentially random variable, with mean 1/0.4=2.5 hours.

The parameter λ of the exponential distribution is the inverse of the mean, so its λ=0.4 h^-1.

The probabity that a repair time exceeds k hours can be written as:

P(t>k)=e^{-\lambda t }=e^{-0.4t}

(a) the probability that a repair time exceeds 3 hours?

P(t>3)=e^{-0.4*3}=e^{-1.2}= 0.30

(b) the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours?

The exponential distribution has a memoryless property, in which the probabilities of future events are not dependant of past events.

In this case, the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours is equal to the probability that a repair takes at least (10-9)=1 hour.

P(t>10|t>9)=P(t>1)

P(k>1)=e^{-0.4*1}=0.67

You might be interested in
A car's speedometer has a percent error of 5%. The speedometer currently shows that the car is traveling at a speed of 60 mph.
kap26 [50]

Answer:

The actual speed of the car would be 57mph

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Which functions are the same as their inverse functions
11Alexandr11 [23.1K]

Answer:

we need to so the functions

Step-by-step explanation:

8 0
3 years ago
Ned counts by fives . he starts at 80 . which number should he say next ?
hodyreva [135]

The next answer is 85.

Counting by five is the same as adding 5 to the number he starts with.

Therefore, 80 + 5 = 85

5 0
3 years ago
The perimeter of a rectangle is 156 inches. The length of the rectangle is five times its width. Find the area of the rectangle.
svlad2 [7]

Answer:

a.

Step-by-step explanation:

i think

8 0
2 years ago
the formula P = 2l + 2w ives the promoter P of a rectangular room with length l and width w. A rectangular living room is 26 ft
jonny [76]

Answer:

Therefore the Perimeter of the room is 94 ft.

Step-by-step explanation:

Given:

P=2l+2w

Where ,

P = Perimeter

l = Length = 26 ft

w = Width = 21 ft

To Find:

Perimeter of the room = ?

Solution:

Perimeter of Rectangle is given as

P=2l+2w

Substituting 'l' and 'w' we get

P=2\times 26+2\times 21=52+42=94\ ft

P=94\ ft

Therefore the Perimeter of the room is 94 ft.

5 0
3 years ago
Other questions:
  • Which of the following best describes the solutions to the inequality shown below?
    14·1 answer
  • 7 times as many 3,073
    9·2 answers
  • 1/2(4x-2)-2/3(6x+9<4
    13·1 answer
  • Multiply the square root of 20 and the square root of 63
    12·2 answers
  • PLZ HELP
    13·1 answer
  • Ernesto brought plastic tubes that are each 5.3 meters long. If Ernesto makes a line of 18 tubes by placing the end-to-end, how
    14·1 answer
  • A construction crew is lengthening a road. The road started with a length of 51 miles, and the crew is adding 3 miles to the roa
    14·1 answer
  • The value of the expression 2³ + 3²-3 x 4 - 5² ÷ 5 + (7 x 4) is.
    9·1 answer
  • How is 1.03 written as a percent?
    13·1 answer
  • Is –8 − –95 positive or negative?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!