1) Assume that there is a mayoral election coming up in a certain city and 53% of the voters in the city support a certain candidate. A sample of 455 voters is polled, and the proportionp^

of voters who support the candidate is calculated.

Find the probability that proportion of voters in the sample who support the candidate is within 5% of the assumed population proportion of 53%.

Round your answer to 4 decimal places.

2) Approximately 15% of the population is left-handed. Assume that a sample of 244 people is selected and the sample proportionp^

of left-handed individuals is calculated.

Find the probability that proportion of people in the sample who are left handed is within 3% of the true population proportion.

Round your answer to 4 decimal places.

3) Approximately 70% of high school students in the United State graduate within 4 years. Suppose a random sample of 58 high school students who were scheduled to graduate last year is obtained, and the proportionp^

of students who graduated within 4 years is calculated.

Find the probability thatp^

is greater than 0.8.

Round your answer to 4 decimal places.

4)Approximately 37% of people in the United State have a blood type of O+. Assume that a sample of size 165 is drawn and the proportionp^

of individuals in the sample with type O+ blood is calculated.

Find the probability that sample proportion is within 0.02 of the true population proportion.

Round your answer to 4 decimal places.

5)

A mortgage company classifies its borrowers into three categories: Low Risk, Medium Risk, and High Risk. From experience, the company knows that:

• 3% of low risk borrowers eventually default on their mortgages.
• 8% of medium risk borrowers eventually default on their mortgages.
• 13% of high risk borrowers eventually default on their mortgages.

The mortgages for 123 high risk borrowers are put together into one portfolio. The company determines that they will profit on the portfolio as long as no more than 18% of borrowers with mortgages in the portfolio default. What is the probability that the company makes a profit on the portfolio?

Round your answer to 4 decimal places.