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
ipn [44]
3 years ago
8

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0

.9. What is (a) the probability that a repair time exceeds 8 hours? 1-e^(1/0.9*8) (b) the conditional probability that a repair takes at least 13 hours, given that it takes more than 9 hours? Note: You can earn partial credit on this problem. Your score was recorded. You have attempted this problem 3 times. You received a score of 0% for this attempt. Your overall recorded score is 0%. You have unlimited attempts remaining.
Mathematics
1 answer:
Pepsi [2]3 years ago
8 0

Answer:

The probability that a repair time exceeds 8 hours is P(X>8)\approx 0.000746586

The conditional probability that a repair takes at least 13 hours, given that it takes more than 9 hours is  P(X\geq 13 | X>9)\approx 0.0273237376

Step-by-step explanation:

A continuous random variable X is said to have an exponential distribution with parameter \lambda > 0 shown as X \sim Exponential(\lambda), if its probability density function is given by

f_X(x)=\begin{cases}\lambda e^{-\lambda x} & x > 0\\ 0 &\text{otherwise}\end{cases}

Let X denote the time require to repair a machine.

(a) The probability that a repair time exceeds 8 hours;

P(X>8)=1-P(X\leq 8)\\P(X>8)=1-\int\limits^8_0 {0.9e^{-0.9x}} \, dx \\P(X>8)=1-0.999253\\P(X>8)\approx 0.000746586

(b) The conditional probability that a repair takes at least 13 hours, given that it takes more than 9 hours;

We want to find P(X\geq 13 | X>9).

P(X\geq 13 | X>9)=\frac{P(X\geq 13)}{P(X>9)} \\\\P(X\geq 13 | X>9)=\frac{\int\limits^{\infty}_{13} {0.9e^{-0.9x}} \, dx}{\int\limits^{\infty}_{9} {0.9e^{-0.9x}} \, dx}\\ \\P(X\geq 13 | X>9)=\frac{8.29382\times10^{-6}}{0.000303539} \\\\P(X\geq 13 | X>9)\approx 0.0273237376

You might be interested in
A negative number divided by a positive number is:
Verdich [7]

Answer:

When you divide a negative number by a positive number then the quotient is negative.

Step-by-step explanation:

hope this helped

7 0
3 years ago
Sarah buys 2 candy bars for $1.45. how much would one candy bar cost
sattari [20]
2 = $1.45
1 = $0.725

anything to ask please pm me
4 0
3 years ago
What are the x-intercepts for x2 + x - 6 = 0? (hint: factor first) please I need this asap
Nezavi [6.7K]
2 negative three.....use Math-way
5 0
3 years ago
Charlie and Andy solve this problem in two different ways.
hammer [34]
Subtracted then divided
5 0
3 years ago
One glass of milk provides 305mg of calcium. Maggie drinks one glass of milk every morning. How many grams of calcium does Maggi
Komok [63]
She drinks 4.27 grams on calcium in 14 days at one glass of milk containing 14 mg per day
8 0
3 years ago
Read 2 more answers
Other questions:
  • Daniel had $28 to spend at the fair. If the admission to the fair is $8 and the rides cost $2
    8·1 answer
  • PLEASE HELP!! would appreciate it
    7·1 answer
  • Lashonda worked for 13 hours each day for 5 days. Then the next day she worked 6 hours. How many hours did Lashonda work in all?
    7·1 answer
  • a company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. what is the approxima
    9·1 answer
  • A group of students bakes 100 cookies to sell at the school bake sale. The students want to ensure that the price of each cookie
    14·1 answer
  • 15 points -Christina went to a soap box derby race with 12 coins in her pocket that totaled to $1.20 what could those coins be ?
    8·1 answer
  • The poetry club had its first bake sale, and they made $79.35. The club members are planning to have
    6·2 answers
  • Please help marking brainliest if its correct!
    7·1 answer
  • Is y=19x - 5 proportional
    6·2 answers
  • Find the area of triangle ABC Remember, the distance between two points is <img src="https://tex.z-dn.net/?f=d%3D%5Csqrt%28x_%7B
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!