SOLUTION: Do I use the z-score equation to solve this, if not, please show me the correct one and explain the steps to the solution. Thanks, 28. It is known that in the absence of

Question 1040610: Do I use the z-score equation to solve this, if not, please show me the correct one and explain the steps to the solution.
Thanks,

28. It is known that in the absence of treatment, 72% of the patients with a certain illness will improve. The Central Limit Theorem tells us that the percentages of patients in groups of 500 that improve in the absence of treatment are approximately normally distributed. Find the percentage of patients (in groups of 500 patients) that have less than a 69% chance of improving in the absence of treatment. Use the percentile z-score table to assist you.
A) 97.72%
B) 6.68%
C) 2.28%
D) 93.92%

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Binomial mean is np=0.72*500=360
Variance is np(1-p)=360*0.28=100.8
sd is sqrt (100.8)=10.04
69% of 500 is 345.
This becomes a problem where the z= (x-mean)/sd, with x=345, mean 360, and sd 10.04
z<(-15/10.04)=-1.494
This is .0676. B is the choice. If I use 10 as the SD, and not 10.04, I get 6.68%
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