1. A random sample of 73 measurements is drawn from a binomial population with probability of success 0.3.

Find P(\hat{p} > 0.32)P(p^>0.32).

The probability that \hat{p}p^ is greater than 0.32 is . (Round to four decimal places as needed.)

2. A study of full-time workers in a certain field found that only about 3% leave their jobs in order to retire. Assume this is the true proportion of all full-time workers in the field who leave their jobs in order to retire. In a random sample of 1100 full-time workers in the field, let \hat{p} p represent the sample proportion who leave their jobs in order to retire.

Find the probability that greater than 1.8% of the sampled full-time workers leave the job in order to retire.

(Round to three decimal places as needed.)

3. A study of full-time workers in a certain field found that only about 3% leave their jobs in order to retire. Assume this is the true proportion of all full-time workers in the field who leave their jobs in order to retire. In a random sample of 1100 full-time workers in the field, let \hat{p}p^ represent the sample proportion who leave their jobs in order to retire.

Find the probability that less than 4% of the sampled full-time workers leave the job in order to retire.

(Round to three decimal places as needed.)

4. A study of full-time workers in a certain field found that only about 3% leave their jobs in order to retire. Assume this is the true proportion of all full-time workers in the field who leave their jobs in order to retire. In a random sample of 1100 full-time workers in the field, let \hat{p}p^ represent the sample proportion who leave their jobs in order to retire.

Describe the properties of the sampling distribution of \hat{p}p^.

The mean of the sampling distribution of \hat{p}p^ is . (Round to two decimal places as needed.) The standard deviation of the sampling distribution of \hat{p}p^ is . (Round to four decimal places as needed.)

5. According to a poll of adults, about 40% work during their summer vacation. Now consider a random sample of 600 adults. Complete the following parts.

What is the probability that over 45% of the sampled adults work during summer vacation?

The probability is . (Round to four decimal places as needed.)

6. According to a poll of adults, about 40% work during their summer vacation. Now consider a random sample of 600 adults. Complete the following parts.

What is the probability that between 37 % and 43 % of the sampled adults work during summer vacation?

The probability is . (Round to four decimal places as needed.)