12 6 Yasmine is investigating the effectiveness of some home cures for hiccups, such as drinking water, being startled, or biting on a lemon. She plans to run 500 trials using a large sample of volunteers. Her experiment runs as follows. Yasmine induces hiccups on a volunteer and starts a timer. After a minute, she tries to ‘cure’ the hiccups using one of the methods, then observes whether the hiccups have stopped. (a) State the conditions under which the Poisson distribution would be a suitable model for the number of hiccups in the first minute. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Yasmine decides that the Poisson distribution is a suitable model, and she calculates that the mean number of hiccups in the first minute for the sample of volunteers is 8.5 After drinking water, Volunteer A hiccups only 2 times in the next minute. (b) Assuming that the cure has not worked, and that hiccups are still occurring at this constant rate, find the probability that a volunteer would hiccup 2 times or fewer. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ After being startled, Volunteer B does not hiccup for 30 seconds (half a minute). (c) Assuming that the cure has not worked, and that hiccups are still occurring at this constant rate, find the probability that a volunteer would not hiccup for the first 30 seconds. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________