An exercise gym opens at 6:00 a.m. every day. The manager decides to use a questionnaire to gather the opinions of the gym members. The first 30 members arriving at the gym on a particular morning are asked to complete the questionnaire.
What is the intended population in this context?
What type of sampling is this?
How could the sampling process be improved?
A baker sells \(3 \cdot 5\) birthday cakes per hour on average.
State, in context, two assumptions you would have to make in order to model the number of birthday cakes sold using a Poisson distribution.
Using a Poisson distribution and showing your calculation, find the probability that exactly 2 birthday cakes are sold in a randomly selected 1-hour period.
（c）Calculate the probability that，during a randomly selected 3 －hour period，the baker sells more than 10 birthday cakes．
（d）The baker sells a birthday cake at 9：30 a．m．Calculate the probability that the baker will sell the next birthday cake before 10：00 a．m．
Select one of the assumptions in part (a) and comment on its reasonableness.