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

0.740.74.

Suppose that a random sample of

100100

people is obtained. Complete parts (a) through (e) below

(c) Describe the sampling distribution of

ModifyingAbove p with caretp,

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

than 5% of the population size and

np(1minusp)equals=19.2419.24greater than or equals10,

the distribution of

ModifyingAbove p with caretp

is

approximately normal

with

mu Subscript ModifyingAbove p with caret Baseline equalsp=0.740.74

and

sigma Subscript ModifyingAbove p with caret Baseline equalsp=0.0440.044.

(Round to three decimal places as needed.)Part 4(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

0.7878?

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

0.7878

is

0.18140.1814.

(Round to four decimal places as needed.)Part 5(e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that

6666

or fewer people in the sample are satisfied with their lives?The probability that

6666

or fewer people in the sample are satisfied is

enter your response here,

which

is

is not

unusual because this probability

is not

is

less than

50

0.5

5

0.05

%.

(Round to four decimal places as needed.)