Question 1118857: The most recent Census Bureau data shows that 22% of eligible voters aged 18-24 voted.
A random sample of eligible 100 voters aged 18-24 is surveyed.
Answer the following questions using the standard normal approximation of the binomial distribution. Round all answers to 4 decimal places. Use STAT TABLES, if necessary.
What is the probability that fewer than 20 voted?
What is the probability that at least 25 voted?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
the mean will be np which is 22
the variance is np(1-p) which is 22*0.78 or 17.16
the sd is the sqrt IV)=4.14
For fewer than 20, want 19.5 for x
z=(19.5-22)/4.14=-2.5/4.14=-0.6035
probability z is less than that is 0.2743, using -0.60 for z.
at least 25 voted uses n>24.5
z=(24.5-22)/4.14=+0.6035 or a probability of 0.2743
can check using exact binomial
n=16 prob 0.0350 from 100C160.22^16*0.78^84
n=17 prob 0.0487
n=18 prob 0.0634
n=19 prob 0.0772
n=15 prob 0.0233
n=14 prob 0.0144
n=13 prob 0.0082
These are 0.2702 with a little more from lower values, so answer is reasonable.
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