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?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

(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

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

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. What is the probability it will still be operating after 3000 hours of service? What is the probability that it will fail prior to 6000 hours of service? If it has been running for 3000 hours, what is the probability it will still be running 2000 hours later?

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...

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 lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose...

The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose we have an iid sample of size 100 of these components Some hints: P(X < c) for an exponential(lambda) can be found via pexp(c,lambda) E[X] = 1/lambda and Var[X] = 1/lambda^2 Round all answers to 4 decimals Using the exact probability distribution, what is the probability that a single component will be within 15.38 units of the population mean? Using Chebyshev's inequality, what is...

The life times, YY in years of a certain brand of low-grade lightbulbs follow an exponential...

The life times, YY in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.55 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise. Part a) Find the probability to 3 decimal places that the first success occurs in the fifth observation. Part b)...

Lithium cellphone batteries for a certain model has a lifetime that follows an exponential distribution with...

Lithium cellphone batteries for a certain model has a lifetime that follows an exponential distribution with β = 3000 hours of continuous use. What is the probability that a randomly chosen battery would last at least 8 months? (assume 30 days in each month) 0.9920 c. 0.8253 e. 0.1466 0.9197 d. 0.8534 What is the probability that a randomly chosen battery lasts between 60 to 8 months? 0.0435 c. 0.0795 e. 0.1466 0.0903 d. 0.1457 What would be the lower...

3. The life of a pump follows an exponential distribution with an average life of 800...

3. The life of a pump follows an exponential distribution with an average life of 800 hours. [10] a) What is the probability that he will die after 900 hours. [10] b) If the pump has worked for 750 hours without failure, what is the probability that it will fail in the next 100 hours. show steps clearly please

The average life of a certain type of motor is 10 years with a standard deviation...

The average life of a certain type of motor is 10 years with a standard deviation of 2 years. You are interested in measuring the life time of this motor by conducting a survey asking customers’ experiences. a.) After a month-long survey, you collect 146 responses. What is the probability that the average life time of the motor is greater than 10 years and 6 months? b.) After a month-long survey, you collect 367 responses and find that the average...

Subjects