According to astudy, the proportion of people who are satisfied with the way things are going in their lives is 0.78. Suppose that a random sample of 100 people is obtained. Complete parts(a) through(e) below.

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(a) Suppose the random sample of 100 people isasked, "Are you satisfied with the way things are going in yourlife?" Is the response to this question qualitative orquantitative? Explain.

A.

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

B.

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

C.

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

D.

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

(b) Explain why the sampleproportion,

p, is a random variable. What is the source of thevariability?

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

no more

no less

than5% of the population size and np(1p)=

nothing

10, the distribution of

p is

approximately normal

skewed left

skewed right

uniform

with

p=

nothing

and

p=

nothing

.

(Round to three decimal places asneeded.)

(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 0.82?

The probability that proportion who are satisfied with the way things are going in their life exceeds 0.82 is

nothing

.

(Round to four decimal places asneeded.)

(e) Using the distribution from part(c), would it be unusual for a survey of 100 people to reveal that 70 or fewer people in the sample are satisfied with theirlives?

The probability that 70 or fewer people in the sample are satisfied is

nothing

, which

is not

is

unusual because this probability

is not

is

less than

0.05

50

0.5

5

%.

(Round to four decimal places asneeded.)