A textile producer has established that a spinning machine stops randomly due

to thread breakages at an average rate of 5 stoppages per hour. What is the

probability that in a given hour:

i) 3 stoppages will occur on this spinning machine?

ii) at most 2 stoppages will occur on this spinning machine?

iii) more than 4 stoppages will occur on this spinning machine?

iv) between 2 and 6 stoppages will occur on this spinning machine?

v) What is the probability that no more than 1 stoppage will occur in a given

two-hour interval?

2. The arrival of patients at a rural clinic is 2 per hour. In any given hour what is

the probability that:

a) no patient will arrive?

b) exactly six patients will arrive?

c) not less than 2 patients will arrive.

d) Determine the variance.