Pauline frequently uses a social networking website to chat with her friends in the evening. On this

Question

Pauline frequently uses a social networking website to chat with her friends in the evening. On this site, she has a total of $120$ friends. If she logs on to the site at $9.30$ pm, on average, $35$% of her friends will also be logged on to the site. Pauline logs on to the site at $9.30$ pm on a particular day. The number of her friends who are also logged on to the site is denoted by $L$. State, in context, two assumptions needed for $L$ to be well modelled by a binomial distribution. Explain why one of the assumptions stated in part (i) may not be valid in this context. Assume now that these assumptions do in fact hold. If $8$ of her friends on this site are chosen at random, find the probability that more than half of them are logged on to the site.

Accepted Answer

(i) The two assumptions are: 1. Friends are logged on to the site independently. 2. The probability that any one friend is logged onto to the site is the same ($0.35$). (ii) The first assumption mentioned in part (i) may not be valid as the log-ons of her friends may not be independent as her friends may be out together or arrange to chat on the site etc. The second assumption mentioned in part (i) may not be valid as the probability of log-on may vary from person to person because of different lifestyles and schedules etc. (iii) $0.106$ ($3$ s.f.)

Binomial Distribution - Binomial Distribution - General

Binomial Distribution - Binomial Distribution - General