Russell is an amateur snooker player. He practises a particular pot several times and the probability of
making the pot each time is 0.3. In any one practice session, his goal is to make the pot 8 times. You may
assume that his probability of making the pot remains constant and all attempts at the pot are
In one week, he has 25 practice sessions and achieves his goal each time.
Estimate the probability that his average number of shots in each session was less than 25.
I assumed this was a negative binomial with X~NB(8,0.3) as probability of success is 0.3 and he needs to pot it 8 times. I assume that I’m meant to find P(X is less the or equal to 24) but I don’t have a formula for cumulative negative binomial and when I tried adding up the probabilities it was quite far off. The answer is 0.145. I’m not sure where I have gone wrong with this. Any help would be appreciated. Thanks