point(s) possible According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.74. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. (a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. OA. The response is quantitative because the number of people satisfied can be counted. OB. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. OC. The response is qualitative because the number of people satisfied can be counted. OD. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. (b) Explain why the sample proportion, p, is a random variable. What is the source of the variability? O A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. C. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. OD. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is with P pis than 5% of the population size and np(1 - p)= | 10, the distribution of p is and = (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.78? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.78 is (Round to four decimal places as needed.) (e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 68 or fewer people in the sample are satisfied with their lives? The probability that 68 or fewer people in the sample are satisfied is which unusual because this probability less than %.