(1) Find the value of c. (2) Find the cumulative distribution function of X. (3) Find the probability that the watch has an operational lifetime in excess of 4 years.
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- Which of the following is a valid cumulative distribution function? Note: the arrow means the line extends to +inf.Prob-2 The diameter of metal cylinder has a probability density function of f(x)=1.5-6(x-50.0)² [mm] 500 metal cylinders delivered to engine assembely plant... How many cylinders' diameters, D< 50.0 mm ? Sol:The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 10 minutes. (a) Find the probability that the time interval between two successive barges is more than 15 minutes. (b) Find a time interval t such that we can be 75% sure that the time interval between two successive barges will be greater than t. Show word count Next
- Can I get help with just parts C and D please.In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) (a) Φ(c) = 0.9850 (b) P(0 ≤ Z ≤ c) = 0.2995 (c) P(c ≤ Z) = 0.1314 (d) P(−c ≤ Z ≤ c) = 0.6528 (e) P(c ≤ |Z|) = 0.0128 You may need to use the appropriate table in the Appendix of Tables to answer this question.The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 12 minutes. (a) Find the probability that the time interval between two successive barges is more than 8 minutes. (b) Find a time intervalt such that we can be 90% sure that the time interval between two successive barges will be greater than t. Loount ▼
- Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?The time intervals between cars that successively pass a toll booth have an exponential distribution with a mean of 8 minutes. Find a time interval t in minutes such that we can be 95% sure that the time interval between two successive cars passing through the toll booth will be greater than t. Round to 2 decimal placesStudents arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.b. Again assuming one advisor, what is the probability that there are more than tenstudents in the clinic at a random point in time? What is the probability that the timespent in the clinic exceeds 30 minutes?.
- The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 10 minutes. (a) Find the probability that the time interval between two successive barges is less than 8 minutes. (b) Find a time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t.For any number of x, the cumulative distribution function (F(x)) is the probability that the observed value of the X will be at most x. Select one: True Falsemin {X1, X2}. %3D Suppose that X1, X2 are iid, and X1 Exp(2). Find the distribution of X(1)