A pacemaker is a medical device that uses electrical impulses, delivered by electrodes contracting the heart muscles, to regulate the beating of the heart. Pacemaker implantation is a necessary treatment for patients who suffer from severe bradycardia (a condition where resting heart rate is less than 40 beats per minute (BPM), which is considered abnormal). A cardiac surgeon at St. Paul's Hospital in Vancouver was conducting research on survival times (i.e. time from a patient's pacemaker surgery until his/her death) from 6807 patients who were implanted a pacemaker between the years 2001 and 2013. The surgeon has found that the survival times (measured in months) follow approximately a normal distribution with mean 101.9 months and standard deviation of 34 months. a) What percentage of patients survived between 77 and 89 months? [3] b) Patients with a survival time in the top 27% require pacemaker replacement. What survival time must a patient reach in order to have a pacemaker replacement? [2]

Q2. [8 marks] The amount of time the university professors devote to their jobs per week has a Normal distribution with an average of 52 hours and a standard deviation of 6 hours. a) Identify the subjects of interest. [1] b) Provide a description of the variable of interest and identify the type of the variable. [1] c) Identify the statistic of interest and the notation. [1] d) If three professors are randomly selected, what is the sampling distribution of the statistic defined in part (c)? [3] e) If three professors are randomly selected, what is the probability that the sample average amount of time they work is more than 60 hours per week? [2] STAT 4800 - Summer 2021 2

Q3. [9 marks] A psychologist believes that 80% of male drivers continue to drive when they are lost, hoping to find the location they seek rather than asking for directions. To examine this belief, he took a random sample of 350 male drivers and they were asked what they did when lost. a) Identify the subjects of interest. [1] b) Provide a description of the variable of interest and identify the type of the variable. [1] c) Identify the statistic of interest and the notation. [1] d) What is the sampling distribution of the statistic defined in part (c)? Note: Make sure you check all the necessary conditions. [4] e) Find the probability that less than 75% of male drivers (from a random sample of 350 men) said they would continue to drive when they are lost. [2]