MATH 216 Computer Oriented Approach to Statistics (Assignment 3A) Questions and Answers Athabasca University

MATH 216 Computer Oriented
Approach to Statistics (Assignment
3A) Questions and Answers
Athabasca University

, lOMoAR cPSD| 43283024




Problem 1. Heart transplants
Past statistics suggest that the “success rate” (survival rate five years after the transplant) of heart transplants is
about 75%. If one randomly selects ten patients who have just received a heart transplant, find the probability
that:
Solution:
x n−x
P (X) = nCx p q
The values of n, p, q, and x are:
N = 10, p = 0.75, q = 0.25, and x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
a. all ten patients survive [2 marks]
10!
P (10) = 10C10 (0.75)10 (0.25)0 = (0.75)10 (0.25)0 = 1 (0.75)10
(10− 10) ! 10!
(0.25)0 = 0.0563
b. zero patients survive [2 marks]
10 !
P (0) = 10C0 (0.75)0 (0.25)10 = (0.75)0 (0.25)10 = 1(0.75)0
( −0) ! 0 !
10
(0.25)10 = 0.0000
c. at most 4 patients survive [2 marks]
First Step:
10 !
P (0) =10C10 (0.75)0 (0.25)10 = (0.75)0 (0.25)10 = 1(0.75)0
( −0) ! 0 !
10
(0.25)10 = 0.0000
P(1) = C 1 9 10. 9 ! 1 9
= 1 9
=
=
(0.75) (0.25) (0.75) (0.25) (0.25)
(10−1)! 1! 10(0.75)
10 1


0.0000
P(2)= C 2 8 110.9 . 8 ! 2 8
=
2 8
= 0.0004
=
(0.75) (0.25) (0.75) (0.25) 45 (0.75) ( 0.25)
10 2
(10−2) ! 2!
10.9 .8 .7 !
P(3)= C
3 7
= (0.75)3(0.25)7 = 3 7
= 0.0031
10 3 (0.75) (0.25) (10−3) ! 3 ! 120(0.75) (0.25)
10.9 .8 .7 . 6 !
P(4)= C 4 6
= (0.75)4 (0.25)6 = 4 6
10 4 (0.75) (0.25) ( 10−4 )! 4 ! 210(0.75) ( 0.25) =0.0162
Second Step:
P(x ≤ 4 ¿=P(0)+ P(1)+ P (2)+ P( 3)+ P( 4)
≈0.0000+0.0000+0.003+0.016
≈0.0190
d. more than 7 patients survive [2 marks]
First Step:




2 Mathematics 216/ Assignment 3