Suppose a certain study reported that 27.7% of high school students smoke. Random samples are selected from high school that has 632 students. (i) If a random sample of 60 students is selected, what...

Suppose a certain study reported that 27.7% of high school students smoke. Random samples are selected from high school that has 632 students.

(i) If a random sample of 60 students is selected, what is the probability that fewer than 19 of the students smoke?

(ii) If a random sample of 75 students is selected, what is the probability that more than 17 of the students smoke?

iii) Explain how to identify the minimum sample size needed to construct a confidence interval for the proportion with a specific margin of the error when the population proportion is unknown.

(iv) A random sample of 175 registered voters revealed that 54% of them voted in the last election. Construct a 95% confidence interval to estimate the true proportion of voter turnout.

(v) A pilot sample of 50 voters found that 30 of them voted in the last election. How many more voters must be sampled to construct a 95% interval with a margin of error equal to 0.04?