5. A sample of n = 2000 parts is pulled from a process every 8 hours and inspected. If fewer than 6 defective parts are found the process is left to run (i.e. c = 5). Otherwise it is stopped until a problem can be found. If the process fraction defective is p = 0.001: a. Find the exact probability of letting the process run. (Hint: Use Calc> Probability Distributions> Binomial in MINITAB or Excel's binomdist() function from the list of statistical functions.) b. Find the approximate probability of letting the process run using the Poisson approximation. c. Find the error of the estimate.

Find the probability that the sample mean of Xbar = 20 hours, as observed here, less than or equal 20 hours could arise if the true mean of the lot

The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter  ?y  for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?

The time it takes to complete an online survey is uniformly distributed over the range of 10.1 minutes to 16 minutes. Calculate the probability that it takes a person between 11.2 and 11.9 minutes to complete the survey.