16 According to a hospital administrator historical records

16. According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted.
What is the probability that at least 70 patients will not be satisfied with the after-surgery care?

A. 89.44
B. 39.44
C. 10.56
D. 78.88
E. 84.49

Solution

P(dissatisfied)=0.2

P(satisfied)=1-0.2=0.8

Among 400 hospital patient,dissatisfied patient:

K=0.2*400=80

P(70 not satisfied)=0.2⁷⁰ * 0.8¹⁰ C(80,70)=p1

P(71 not satisfied)=0.2⁷¹ * 0.8⁹ C(80,71)=p2

P(72 not satisfied)=0.2⁷² * 0.8⁸ C(80,72)=p3

P(73 not satisfied)=0.2⁷³ * 0.8⁷ C(80,73)=p4

P(74 not satisfied)=0.2⁷⁴ * 0.8⁶ C(80,74)=p5

P(75 not satisfied)=0.2⁷⁵ * 0.8⁵ C(80,75)=p6

P(76 not satisfied)=0.2⁷⁶ * 0.8⁴ C(80,76)=p7

P(77 not satisfied)=0.2⁷⁷ * 0.8³ C(80,77)=p8

P(78 not satisfied)=0.2⁷⁸ * 0.8² C(80,78)=p9

P(79 not satisfied)=0.2⁷⁹ * 0.8¹ C(80,79)=p10

P(80 not satisfied)=0.2⁸⁰ * 0.8⁰ C(80,80)=p11

P(at leat 70 not satisfied after surgery)=p1+p2+p3+p4+p5+p6+p7+p8+p1+p10=.8944

Percentage is 89.44%