4. The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter 0= 4. What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 1 hours?
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- 4. In professor Shankar's quiz, the time taken to complete the quiz is a random variable with a pdf £x (x) = 20 = exp(-26 ) ₁ x 20² 20 1₂x ≥0 What is the average time for completion? If there are 50 students in the class, what is the probability that at least 20 of them will complete the quiz in less than the average? What is the probability that exactly 35 students complete within the average time.The lifetime (in years) of a washing machine from a particular company is an exponential random variable with parameter 1/5 . The company offers to replace any machine which breaks within 6 months. (a) What proportion of machines do they need to replace. (b) What is the expected time until a customer needs to buy a new machine? (Each time the company replaces a machine which breaks within 6 months, the company agrees to replace the new machine if it breaks within 6 months.)the time it takes a person to wash the dishes is uniformly distributed between 10 minutes and 16 minutes. What is the probability that a randomly selected event of washing dishes will take a person between 12 and 13 minutes ?
- Elizabeth is a busy pediatrician. On any given day, she diagnoses an average of five babies with middle-ear infections. Assume that the number of babies who come to her clinic with middle-ear infections is a Poisson random variable. Calculate the probability that fewer than three babies with middle-ear infections will come to her clinic tomorrow. Give your answer in decimal form precise to three decimal places. P(X < 3) =CHAPTER 5 TEXTBOOK Section 5.18- Exercise 20 Let X be the number of bacterial colonies per cubic centimeter, a Poisson random variable with expected value 3. (i) What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter? (ii) What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where there is at least one bacterial colony? (iii) How many cubic centimeters must be observed for the probability of observing at least one with at least one bacterial colony to be 0.95? 0.9999997 ÷ What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter? What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where 0.9502 there is at least one bacterial colony? How many cubic centimeters must be observed for the probability of observing at least one with at least one 1 bacterial colony to be 0.95?11% of US adults eat fast food 4 to 6 times per week. You randomly select 12 US adults. Find the probability that the number of US adults that eat fast food 4 to 6 times per week is less than three.
- The service time for a passport application in a certain government office is modelled as an exponential random variable with parameter λ = 5 per hour, independent and identically distributed for all applicants. Determine the probability that 50 applicants is accommodated within eight hours. Determine the maximum number of applicants such that the chance of accommodating all of them within eight hours is at least 95%.A G's production of 950 manufactured parts contains 70 parts that do not meet the customer requirements . Two parts are selected randomly without replacement from the batch. What is the probability that the second part is defective given that the first part is defective?The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, the probability that 38 or more will not develop any faults within the first 3 years of use is ....
- An average of 1 package is sent to a server in 1 second. The server, on the other hand, prepares a document using the 5 packages received. The time between packets is modeled as an exponential random variable. Let X be a random variable expressing the time it takes the server to prepare a document. The time taken to prepare a document; a) Find the probability that it is more than 10 seconds.(with detail) b) Find the probability that it is between 5 seconds and 10 seconds. (with detail)We take the point of view that x (measured in days as units) is a continuous random variable. Suppose a fatal airline accident has just been reported on the news. What is the probability that the waiting time to the next reported fatal airline accident is the following? (a) less than 20 days (b) more than 50 days (c) between 30 and 70 days10. An atom of Uranium-238 is unstable and will eventually decay (i.e., emit a particle and turn into a different element). Given an atom of Uranium-238, the time elapsed until it decays, in years, is modeled as an Exponential random variable with parameter 1 = 0.000000000155. How many years must pass for there to be a 50% chance that the Uranium atom decays?