6. In a certain communications system, there is an average of 1.3 transmission errors per 10 seconds. Let the distribution of transmission errors be Poisson. (а). What is the probability of more than 2 errors in a communication 10 seconds in duration? (b). What is the probability of more than 2 errors in a communication 30 seconds in duration?

5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. %3D wg probal b What is the probability that the spider catches at least one insect in 12 hours? PUS 18)

Suppose we have a bucket of 20 balls with 10 red and 10 green. We take 5 draws and after each draw, we remove the chosen ball from the bucket before our next draw (this is called drawing without replacement). Can we use the binomial distribution to model this scenario? Why or why not?

The time between arrivals of customers at the drive-up window of a bank follows an exponential distribution with a mean of 20 minutes. a)What is the probability that the arrival time between customers will be 13 minutes or less? b)What is the probability that the arrival time between customers will be between 13 and 27 minutes?

Suppose that we perform an experiment where we classify the outcome as either a success or a failure. Let the probability of a success be 0.90.9 . Now we want to repeat this experiment n ​= 44 times and let the random variable X count the number of successes. Visualize a probability tree for this situation​ (without actually drawing it​ out).  Round to four decimal places as needed. From each vertex there will be 22  edges going to a success S and a failure F. Since each stage is independent all the edges going to an S will have probability p​ = . 9.9 and all the edges going to an F will have probability q​ = . 10.10. If a single path has 2 success and the rest failures​ (in any​ order) then the probability of that single path is nothing. Note that these 2 successes may be in any of the 44 stages so there are nothingof these paths which have 2 successes.   ​Therefore, ​P(X​ = 2)​ = nothing.

Q5. It was found that a New Brunswick family doctor has on average 14 patients calling in for anappointment they say they need to have on that very day during a standard 10 hour work day.Using the tables(a) What is the probability that a New Brunswick family doctor has more than 20 patientscalling in for an appointment they say they need to have on that very day during a standard10 hour work day?(b) What is the probability that a New Brunswick family doctor has more than 2 patientscalling in for an appointment they say they need to have on that very day during the nexthour?(c) What is the probability that a New Brunswick family doctor has 7 or less 20 patientscalling in for an appointment they say they need to have on that very day during the next3 hours?(d) For this situation, determine the probabilities of being within 1, 2 an d 3 standard deviations for the mean and compare these results to the empirical rule