Chapter 4, Problem 46SE

A USA Today survey of adults aged 18 and older conducted by Princess Cruises asked how many days into a vacation it takes until respondents feel truly relaxed. The responses as follows: 422-a day or less; 181-2 days; 80-3 days; 121-4 or more days; and 201 -never feel relaxed.
  a. How many adults participated in the Princess Cruises survey?
  b. What has the highest probability? What is the probability of this response?
  c.What is the probability a respondent never feels truly relaxed on a vacation?
  d. What is the probability it takes a respondent 2 or more days to feel truly relaxed?

To determine

(a)

To find:

Number of adults participated in the Princess Cruises survey.

Answer to Problem 46SE

Total 1005 adults participated in the Princess Cruises survey.

Explanation of Solution

The responses in table form is shown below. To find probability, simply divide each count by total count (relative frequency method).

Response	Count	Probability
A day or less	422	$\frac{422}{1005}=0.42$
2 days	181	$\frac{181}{1005}=0.18$
3 days	80	$\frac{80}{1005}=0.08$
4 or more days	121	$\frac{121}{1005}=0.12$
Never feel relaxed	201	$\frac{201}{1005}=0.20$
Total	1005

From above table, total 1005 adults participated in the Princess Cruises survey.

To determine

(b)

To find:

Response which has the highest probability and the probability.

Answer to Problem 46SE

Response "a day or less" has the highest probability and the probability.

Explanation of Solution

The responses in table form is shown below. To find probability, simply divide each count by total count (relative frequency method).

Response	Count	Probability
A day or less	422	$\frac{422}{1005}=0.42$
2 days	181	$\frac{181}{1005}=0.18$
3 days	80	$\frac{80}{1005}=0.08$
4 or more days	121	$\frac{121}{1005}=0.12$
Never feel relaxed	201	$\frac{201}{1005}=0.20$
Total	1005

From above table, response "a day or less" has the highest probability of 0.42.

To determine

(c)

To find:

The probability that a respondent never feels truly relaxed on a vacation.

Answer to Problem 46SE

The probability that a respondent never feels truly relaxed on a vacation is 0.2.

Explanation of Solution

The responses in table form is shown below. To find probability, simply divide each count by total count (relative frequency method).

Response	Count	Probability
A day or less	422	$\frac{422}{1005}=0.42$
2 days	181	$\frac{181}{1005}=0.18$
3 days	80	$\frac{80}{1005}=0.08$
4 or more days	121	$\frac{121}{1005}=0.12$
Never feel relaxed	201	$\frac{201}{1005}=0.20$
Total	1005

From above table, the probability that a respondent never feels truly relaxed on a vacation is 0.2.

To determine

(d)

To find:

The probability it takes a respondent 2 or more days to feel truly relaxed.

Answer to Problem 46SE

The probability it takes a respondent 2 or more days to feel truly relaxed is 0.38.

Explanation of Solution

The responses in table form is shown below. To find probability, simply divide each count by total count (relative frequency method).

Response	Count	Probability
A day or less	422	$\frac{422}{1005}=0.42$
2 days	181	$\frac{181}{1005}=0.18$
3 days	80	$\frac{80}{1005}=0.08$
4 or more days	121	$\frac{121}{1005}=0.12$
Never feel relaxed	201	$\frac{201}{1005}=0.20$
Total	1005

From above table, the probability it takes a respondent 2 or more days to feel truly relaxed is:

  $\begin{array}{c}P\left(\text{2 or more days}\right)=P\left(\text{2 days}\right)+P\left(\text{2 days}\right)+P\left(\text{4 or more days}\right)\\ =0.18+0.08+0.12\\ =0.38\end{array}$