Question

Failures in machine in an 8 hrs shift is 1.5 failures. a) probability that in a...

Failures in machine in an 8 hrs shift is 1.5 failures.
a) probability that in a period of 16 hrs, exactly 2 failures take place.
b) probability that number of failures in 8 hrs exceed the media (medium value) in more than 1.5 standard deviations

Homework Answers

Answer #1

Let X: failure in machines in an 8 hrs shift have exponential distribution with 1.5 failures.

a) P(X = 2)

For 16 hours the failure rate is 1.5 * 2 = 3 failures that is

The pdf of exponential distribution is,

The probability that exactly 2 failures takes place is 0.0074

b) P(X more than medium value)

The standard deviation of exponential distribution is,

Medium value is nothing but median.

The median of exponential distribution is,

The distribution function of exponential distribution is,

Probability that number of failures in 8 hours exceed the medium value is 0.422367

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
What is the probability that a normal random variable will take a value that is less...
What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)? .8531 .1468 .9332 .0668 What is the probability that a normal random variable will take a value that is between 1.5 standard deviations below the mean and 2.5 standard deviations above the mean? In other words, what is P(-1.5 < Z < 2.5)? .9938 .0668 .9270 .0730 What is...
3. A mix beverage machine releases a certain amount of syrup into a chamber where it...
3. A mix beverage machine releases a certain amount of syrup into a chamber where it is mixed with carbonated water. The amount of syrup follows a normal distribution with a mean of 1.29 fl.oz. and a standard deviation 0.016 fl.oz. a. Find the probability that a syrup amount does not exceed 1.33 fl.oz. (10) b. Find the probability that a syrup amount is less than 1.29 fl.oz. (10) c. Find the probability that a syrup amount exceeds the mean...
6. You have been provided the following probability distribution: Pets P(x) x*P(x) (x-µ)²P(x) 0 0.330 1...
6. You have been provided the following probability distribution: Pets P(x) x*P(x) (x-µ)²P(x) 0 0.330 1 0.270 2 0.300 3 0.050 4 0.025 5 0.020 6 or more 0.005 Let x = the total number of pets in a household a. Complete table b. What is the probability of a household having no pets? c. What is the probability of a household having exactly 3 pets? d. What is the probability of a household having between 1 and 3 pets?...
What is the probability that the following project will take more than 10 weeks to complete...
What is the probability that the following project will take more than 10 weeks to complete if the activity means and standard deviations are as shown below? (Round standard deviation to 2 decimal places and final answer to 4 decimal places.) Use Table B. Activity Mean Standard Deviation 1-2 5 1.3 2-3 4 1.0 1-3 8 1.6
The sales of medicines in a certain pharmacy behaves with a variable with a normal distribution...
The sales of medicines in a certain pharmacy behaves with a variable with a normal distribution with means of 2000 pesos and variance of 62500 a) What is the probability that the pharmacy will sell more than 1500 pesos? b) How many standard deviations is a sales value of 3300 pesos in the scope of the media? Can it be considered atypical (unusual) or not? Why? c) What is the 99th percentile of sales? d) What is the probability that...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.4 days. Martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.4 day per employee with a standard deviation of 1.6 days. Suppose...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. Martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. Suppose...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of...
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.3 days per employee with a standard deviation of 1.9 days. Martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.4 day per employee with a standard deviation of 1.8 days. Suppose...
Suppose that for a given computer salesperson, the probability distribution of x = the number of...
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 month is given by the following table. x 1 2 3 4 5 6 7 8 p(x) 0.04 0.10 0.13 0.30 0.30 0.11 0.01 0.01 (a) Find the mean value of x (the mean number of systems sold). Answer= 4.14 (b) Find the variance and standard deviation of x. (Round your standard deviation to four decimal places.) variance = 1.8604...
State         Probability                 RA               &
State         Probability                 RA                   RM       1                 10%                         16%                 10%    2                 40%                         7%                   18%    3                 40%                         12%                 -5%    4                 10%                         -8%                 9%   Calculate the expected returns on security A and the market. Calculate the variances and the standard deviations of security A and the market. Calculate the coefficient of variations (CV) for security A and the market. Does A initially seem to be more or less attractive than a market portfolio? Why? What other consideration...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT