7. a recent medical survey reported that 45% of the respondents felt that the doctor explained their condition in a sufficient manner. assuming that this poll reflects all the patients, find the probability that for 12 patients:
a. four or more agree
b. no more than 8 agreed

(a) 0.8655

(b)0.8655

Step-by-step explanation:

X is the number of respodents who agree

P(x ≥4), n=12, p=0.45

P(x ≥4)=1-P(x<4)

P(x<4)=P(0 ≤x<4)= P(0 ≤x≤3)=P(x=0,1,2,3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

P(x ≥4)=1-P(x<4)=1-0.134468=0.8655319

(b)

Y represent those who agree

P(Y≤8), n=12, p=0.45

P(Y≤8)=1-P(Y>8)

P(Y>8)=P(8<Y≤12)=P(9≤Y≤12)=P(Y=9,10,11,12)

Total =0.134468

P=1-0.134468=0.8655319

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.