Question

The number of earthquake tremors in a 12-month period appears to be distributed as a Poisson random variable with a mean of 6. Assume the number of tremors from one 12-month period is independent of the number in the next 12-month period. For the following probability problems provide the probability statement, indicate how to calculate the probability by plugging values in to the equation(s), provide the probability. A) What is the probability that there are at most 4 tremors in 1 year? B) Find the probability that there are 18 tremors in 2 year. C) Find the probability that there are no tremors in a 1-month period? D) What is the probability that the time until the next tremor is between 2 and 4 months away? An online retailer reimburses a customer's shipping charges if the customer does not receive his order within 1 week. Delivery time (in days) is exponentially distributed with a mean of 3.5 days. What percentage of customers have their shipping charges reimbursed? Show all your work

Answer 1

Solution the number of earthquake tremors in a 12 - Month period[x] appears to be distributed as poisson random Variable with a mean of 6. Then , P(x=x) = éb cosa Sa! The probability that there are 10 tremors in 1-year C12-month period) PLX= 10) - et (6)10 = 0.0413 ☆ The probabi lo! The mean tremore for two years, x=2X6=12 . The probability that there are 18 tremors in 2 years, (24 month period) prx=18] = eth(12) " 0.0255 181 © The mean tremore for one-month, = 6 = 1 the probability that there are no tremors in to morth period PCX=o) -e-Y2 1.1/2) • 606

I The mean tremors for one-month, id = 1 X 6=3 the probability that 3 are more than 5 tremors in 6-month period PCX35) -|- PCXL5) 1-0.9161 Cusing excel function = poisson (5,3,1)). = 0.0839