According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. 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.

A.The response is quantitative because the number of people satisfied can be counted.

B.The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.

C.The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

D.The response is qualitative because the number of people satisfied can be counted.

(b) Explain why the sample proportion, p, is a random variable. What is the source of the variability?

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 different people feel differently regarding their satisfaction.

C. 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.

D. 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) 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 ______

1. No less
2. No more

than 5% of the population size and np(1p)= ____ 10,

the distribution of p is _______ with

1. Aproxamotly normal
2. Uniform
3. Skewed left
4. Skewed right

p=____and p= ____ (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 0.83? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.83 is ________ (Round to four decimal places as needed.)

(e) Using the distribution from part (c), would it be unusual for a survey of100 people to reveal that74 or fewer people in the sample are satisfied with their lives?

The probability that 74 or fewer people in the sample are satisfied is _____,

which_____ unusual because

1. Is
2. Is not

this probability _____

1. Is
2. Is not

less than _____%. (Round to four decimal places as needed.)

1. 0.05
2. 50
3. 0.5
4. 5