Question

In: Statistics and Probability

A certain type of pump’s time until failure has an exponential distribution with a mean of...

  1. A certain type of pump’s time until failure has an exponential distribution with a mean of 5000 hours. State answers rounded to two decimal places.
    1. What is the probability it will still be operating after 3000 hours of service?
    2. What is the probability that it will fail prior to 6000 hours of service?
    3. If it has been running for 3000 hours, what is the probability it will still be running 2000 hours later?

Solutions

Expert Solution

TOPIC:Exponential distribution and probabilities.

Now, rounding the answers in two decimals( as needed ), the correct answers are:

a. 0.55

b. 0.70

c. 0.67

(ANSWERS)


Related Solutions

The time until failure for an electronic switch has an exponential distribution with an average time...
The time until failure for an electronic switch has an exponential distribution with an average time to failure of 4 years, so that λ = 1 4 = 0.25. (Round your answers to four decimal places.) (a) What is the probability that this type of switch fails before year 3? (b) What is the probability that this type of switch will fail after 5 years? (c) If two such switches are used in an appliance, what is the probability that...
The lifetime of a certain type of batteries follows an exponential distribution with the mean of...
The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? (Answer: 0.3114) b) Once a battery is depleted, it is replaced with a new battery of the same type. Assumingindependence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? (Answer: 0.2623) c) What is the probability that it takes...
5) The lifetime of a certain type of batteries follows an exponential distribution with the mean...
5) The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? b) Once a battery is depleted, it is replaced with a new battery of the same type. Assuming independence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? c) What is the probability that it takes less than...
(Exponential Distribution) The life, in years, of a certain type of electrical switch has an exponential...
(Exponential Distribution) The life, in years, of a certain type of electrical switch has an exponential distribution with an average life of ?? = 2 years. i) What is the probability that a given switch is still functioning after 5 years? ii) If 100 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?(also Binomial Distribution
Suppose the time to failure follows an exponential distribution with parameter λ. Based on type II...
Suppose the time to failure follows an exponential distribution with parameter λ. Based on type II censoring determine the likelihood and the maximum likelihood estimator for λ. Assume that n = 3 and the experiment ends after 2 failures.
The life, in years, of a certain type of electrical switch has an exponential distribution with...
The life, in years, of a certain type of electrical switch has an exponential distribution with an average life 2 years. If 100 of these switches are installed in different systems, what is the probability that at most 2 fail during the first year?
The waiting time until a courier is received is followed by an exponential distribution with an...
The waiting time until a courier is received is followed by an exponential distribution with an expected waiting time of 5 days. Find the probability that the mean waiting time for the delivery time of 50 couriers exceeds 6 days b. There are 200 questions to an FRCS exam. Suppose the probability of having through question correct is 0.6, no matter other questions. If the cutoff for a grade B is 80%, what is the likelihood of a "B"
The amount of time until a laptop breaks down follows a an exponential distribution which has...
The amount of time until a laptop breaks down follows a an exponential distribution which has the following distribution F(x) =        1 – exp(- ?x),         if x ≥ 0 0                   ,     otherwise The parameter ?=1, the population mean and standard deviations are equal to 1/?. A sample size of n = 32 was generated from the above population distribution for k = 10,000 times. One of these samples is presented in the table below. 2.5689 0.7311 1.6212 0.0021 1.3902 0.0057...
The amount of time until a laptop breaks down follows a an exponential distribution which has...
The amount of time until a laptop breaks down follows a an exponential distribution which has the following distribution F(x) =        1 – exp(- ?x),         if x ≥ 0 0                   ,     otherwise The parameter ?=1, the population mean and standard deviations are equal to 1/?. A sample size of n = 32 was generated from the above population distribution for k = 10,000 times. One of these samples is presented in the table below. 2.5689 0.7311 1.6212 0.0021 1.3902 0.0057...
The time that takes to complete a certain type of construction projects has a mean of...
The time that takes to complete a certain type of construction projects has a mean of 35.5 months and a standard deviation of 1.5 months. a. According to the Tchebysheff’s theorem, at least what percentage of these projects must have taken between 26.5 months and 44.5 months to complete? b. If in addition we are told that the relative frequency curve for the completion times is a bell-shaped curve, then approximately what percentage of these projects would take more than...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT