Practice Question 3: Suppose the time to do a health check (X) is exponentially distributed with an average of 20 minutes. a) What is the parameter of this exponential distribution (2)? b) What is the probability that a health check can be done in less than 15 minutes? c) What is the probability that a health check can be done in more than 25 minutes? d) What is the probability that a health check can be done in between 15 and 25 minutes) e) A health check already took 20 minutes, what is the probability that the health check can be done in less than 30 minutes?

The lifetime, in years, of a certain type of electrical switch has an exponential distribution withan average lifetime of 2 years. Question. For a single system, what is the probability we can keep one switching mechanismoperable for 10 years if we assume we can replace a switch due to failures up to three timesduring the 10-year period?

The time until the graduates of a department find their first jobs after graduation follows an Exponential distribution with mean 10 months. The probability that a graduate of this department will not be able to find a job in 1.5 years is ..........

Let's assume data collected at the Diamond Head State Monument sug- gests that an exponential distribution with mean value 2 hours is a good model for rainfall duration. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?

suppose that on-the-job injuries in a textile mill occur at the rate of 0.1 per day. A, what is the probability that two accidents will occur during the next (five-day) work week? B, in the probability that four accidents will occur over the next two work weeks, the square of your answer to part (a) explain?

I need help with this question, A and C are wrong and I don't know D

It is known to show an exponential distribution where the average lifespan of a type of CPU is ten years. What is the probability that the company that leases the server for ten years will encounter a central processing unit failure within the period of use?

The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.

The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)