If 0.8% of the fuses delivered to an arsenal are defective, use the Poisson approximation to determine the probability that 4 fuses will be defective in a random sample of 400.
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- About 7% of the population has a particular genetic mutation200 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 200If life length ( in hours ) of certain kind of device follows chi - squared distribution with dof 10 . Find the probability that exactly 2 of 6 such devices in a system will have to be replaced within the first 16 hours of operation. Assume that life of the devices are independentA large ski mountain has a fleet of 4 snowmobiles it uses during the winter season. It believes that the time between consecutive repair operations for a single snowmobile is an exponential random variable with a mean of .75 weeks. There are two dedicated technicians that are capable of repairing the snowmobiles. A broken down snowmobile will be repaired by one of these technicians (when one becomes available) and the repair time of a snowmobile can be modeled as an exponential random variable with a mean of .4 weeks. (a) Describe a queueing system model of the repair operations of the snowmobiles by answering the following questions: What are the customers in the queueing system? What are the servers and what service is being provided? b) Provide the rate transition diagram of the birth and death process that captures the queueing system. Be sure to provide λn and µn for each relevant value of n and your logic behind any calculations used to obtain them (c) Provide the…
- Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 107 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities:Each trial in a binomial experiment has a 25% probability of success.if the normal distribution is to be used to calculate a probability for thisbinomial experiment, then number of trials must be at leastA certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.