Question

At a certain university, each student who tries to purchase concert tickets for an upcoming show is successful at connecting to the concert ticket website with probability 0.85. If unsuccessful in logging on, he or she tries again a few minutes later, over and over, until finally getting tickets. The concert is large (tens of thousands of seats), so assume that such attempts are independent. Within a group of 300 students, find the probability that strictly more than 360 attempts are necessary for these 300 students to successfully get tickets.

Answer 1

from Geometric distribtuion:

here for 1 person to get ticket ; expected number of attempt =1/p=1/0.85 =1.176

and std deviation =sqrt((1-p)/p²) =0.4556

hence for 300 person expected attempt =300*1.176=352.94

and std deviation =0.4556*sqrt(300)=7.89

from Normal approxiation and continuity correction:

probability that strictly more than 360 attempts are necessary for these 300 students to successfully get tickets =P(X>360)=P(Z>(360.5-352.94)/7.89)=P(Z>0.96)=0.1685