Statistics help (is this a Z Table thing??)

Question

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 6505 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 75 and 90 months?

b) Patients with a survival time in the top 20% require pacemaker replacement. What survival time must

a patient reach in order to have a pacemaker replacement?

Answer 1

a)

x = number of survival months. x is normally distributed with mean 101.9 and standard deviation 34

we want to find P(75 < x < 90)

z -statistic (x - mean)/SD is N(1,0)

P(75 < x < 90) = P( (75-mean)//SD < z < (90-mean)/SD) =

P((75-101.9/34) < z < (90-101.9)/34) =

P(-0.79 < z < -0.35) =

P(z < -0.35) - P(z < -0.79) = 0.3632 - 0.2148 = 0.1484

b) z = (x - mean)/SD

find z corresponding to 80th percentile (which is top 20 percent) = 0.84

0.84 = (x - 101.9)/34

x = 34(0.84) + 101.9 = 113.46