Question 1061987: Can someone show me how to work out this problem?
A study in a particular state found that only 5% of the voters have Doctoral degrees. In a random sample of 200 voters, let x be the number who have doctoral degrees.
a. What's the mean of x?
b. What's the standard deviation of x?
c. What's the z-score for x > 10.5
d. What is the probability that more than 10.5 voters in a sample of 200 voters will hold a Doctoral degree?
e. What is the probability that at least 10.5 voters in a sample of 200 voters will hold a Doctoral degree?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a. The mean of a proportion is n*p, the probability, so the mean is 200*0.05=10.
b. variance is np*(1-p)=10*(0.95)=9.5
the sd is sqrt (variance)=sqrt (9.5)=3.08
c. z=(10.5-10)/3.08>0.1581.
d.This translates into 0.4372 from the table or calculator. That is the probability of more than 10.5 voters will hold a doctoral degree. The problem with this is that we have to work with 11, not 10.5
so z=1/3.08=0.3247; the probability of z being greater than that is 0.3727.
e. At least 10.5 is mathematically the same as greater than 10.5, because the function is continuous and not discrete. However, this has to be at least 11 voters, and that is the same answer as above.
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