If jobs arrive every 15 minutes on average at the UITS front

If jobs arrive every 15 minutes on average at the UITS front desk, i.e. the rate lambda = 4 per hour. Please suggest a reasonable distribution for the number of jobs arriving between 2pm to 4pm. According to the provided information, specify the corresponding parameter in the distribution. With the above distribution, what is the probability to get 5 jobs within 2 hours? Please suggest a reasonable distribution for the waiting time (hours) to get a job. According to the provided information, specify the corresponding parameter in the distribution. With the above distribution, what is the probability of waiting less than or equal to 30 minutes, i.e. half an hour to get a job?

Solution

2) mean = 4 per hour

we have to find 5 jobs in 2 hour

that means 2,5 jobs per hour

p(x=2.5) = e^(-4)*(4)^2.5/2! = 0.293