A Statistical Consulting Center receives on average 2 new consulting applications per week. ( The Center is open 5 days per week ).
a) Let T be the weekday waiting time (in days) for receiving next applications , which is of the following is true?
A. E [ T ] = 2
B. T ~ Uniform(a = 2, b = 5)
C. T ~ Poi sson ( lambda = 2 . 5)
D. T ~ Exp onential ( lambda = 2 . 5)
E. None of the above
b)
Find P(
1.3 < T < 4)
c)
What is the probability that the Center received 2 applications in one week and 3 applications in the next week?
d) In a three month period, how many new applications would the Center expect to receive?
Assume 4
weeks per month.
e) Given that the Center received 10 cases in 4 weeks, what is probability that 7 of these cases were received either the second or third week (i.e. the middle two weeks)?