Chapter 19, Problem 19.1TY

(a)

To determine

To find: The sample space if the subject is either female or male.

Answer to Problem 19.1TY

The sample space if the subject is either female or male is $S=\left\{\text{Male,}\text{Female}\right\}$.

Explanation of Solution

Given info:

The study deals with the exercise and fitness. The participants are either female or male.

Justification

Sample space:

The set of all possible outcomes of an experiment is known as sample space. The sample space denoted as (S). The number of possible outcomes is denoted as N(S).

Here, the possible outcomes for the study are male and female. One subject is randomly selected can be either male or female.

The sample space is, $S=\left\{\text{Male,}\text{Female}\right\}$.

(b)

To determine

To find: The sample space of the rate of perceived exertion (RPE) after 10 minutes bicycle exercise.

Answer to Problem 19.1TY

The sample space of the rate of perceived exertion (RPE) after 10 minutes bicycle exercise is $S=\left\{6,7,8,\mathrm{...},19,20\right\}$.

Explanation of Solution

Given info:

A study is conducted between the exercise and fitness. The rate of perceived exertion (RPE) measures in whole number from 6 to 20.

Justification

Here, the subject rates of perceived exertion (RPE) are after 10 minutes exercise in bicycle. The RPE ranges between 6 and 20. The number 6 represents no exertion and 20 represents that maximum exertion during bicycle exercise.

Thus, the sample space is $S=\left\{6,7,8,\mathrm{...},19,20\right\}$.

(c)

To determine

To find: The sample space for the maximum volume of oxygen consumed per minute during exercise.

Answer to Problem 19.1TY

The sample space of the maximum volume of oxygen consumed per minute during exercise is $S=\left\{\text{All}\text{values}2.5\le V{O}_2\le 6.1\text{liters}\text{per}\text{minute}\right\}$.

Explanation of Solution

Given info:

The VO₂ is measured during exercise. VO₂ ranges from 2.5 and 6.1 liters per minute.

Justification

Here, VO₂ is the maximum volume of oxygen is consumed during exercise. It ranges from is 2.5 and 6.1 liters per minute. The minimum oxygen consumed during exercise is 2.5 liters per minute and maximum oxygen consumed during exercise is 6.1 liters per minute.

The sample space is $S=\left\{\text{All}\text{values}2.5\le V{O}_2\le 6.1\text{liters}\text{per}\text{minute}\right\}$.

(d)

To determine

To find: The sample space for the maximum heart beat (beats per minute).

Answer to Problem 19.1TY

The sample space of the maximum heart beat (beats per minute) is $S=\left\{\text{All}\text{heart}\text{rates}\text{such}\text{that}\text{heart}\text{rate}>70\text{bpm}\right\}$.

Explanation of Solution

Answers will vary for the maximum heart rate. One of the possible answers is given below:

Given info:

A study is conducted between the exercise and fitness. The maximum heart rate is measured during exercise.

Justification:

The maximum heart rate is recorded for each subject after exercise. Suppose that the lowest maximum heart rate is 70 beats per minute after exercise, hence, the sample space includes all heart rates above 70.

Thus, the sample space of the maximum heart beat (beats per minute) is $S=\left\{\text{All}\text{heart}\text{rates}\text{such}\text{that}\text{heart}\text{rate}>70\text{bpm}\right\}$