Sixty-four percent of voters in a very large electorate support candidate Smith in an upcoming election. A news organization surveys 900 voters chosen at random. Let Y denote the number of voters out of the 900 surveyed voters who support candidate Smith, and let p denote the proportion of voters out of the 900 surveyed voters who support candidate Smith.

1. What is the expected value of Y , i.e., what is E (Y ) ?

2. What is the variance of Y , i.e., what is Var (Y )?

3. What is the standard deviation of Y , i.e., what is SD (Y )?

4. By using a computer software package, what is the exact probability that at least two-thirds of the surveyed voters support candidate Smith, i.e., what is P (Y 600)?

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5. What is the expected value of p , i.e., what is E (p ) ?

6. What is the variance of p , i.e., what is Var (p ) ?

7. What is the standard deviation of p , i.e., what is SD (p ) ?

8. By using the normal distribution, approximate the probability that at least two-thirds of the surveyed voters support candidate Smith, i.e., approximate

P(p0.66667).