R5.5 - Review Exercises 2Drive to exercise : The two-way... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 5: R5.5 - Review Exercises (page 356)

2Drive to exercise : The two-way table summarizes the responses of 120 people to a survey in which they were asked, 鈥淒o you exercise for at least 30 minutes four or more times per week?鈥� and 鈥淲hat kind of vehicle do you drive?鈥�
Exercise Sedan SUV Truck
Yes $25$ $15$ $12$
No $20$ $24$ $24$
Suppose one person from this sample is randomly selected.
a. Find the probability that the person drives an SUV.
b. Find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.
c. Find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week.

Short Answer

Expert verified

(a) Probability that the person drives an SUV is $0.325$ .

(b)The probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week is $0.6$ .

(c)The probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week is $0.33$ .

Step by step solution

Part (a) - Step 1 : Given Information

We are given three different vehicles and if a person exercises or not . We need to find if the person drives an SUV .

Exercise	Sedan	SUV	Truck
Yes	$25$	$15$	$12$
No	$20$	$24$	$24$

Part (a) - Step 2 : Explanation

We need to find the total and divide favorable outcome by total outcomes in order to achieve the probability .

Exercise	Sedan	SUV	Truck	Total
Yes	$25$	$15$	$12$	$52$
No	$20$	$24$	$24$	$68$
Total	$45$	$39$	$36$	$120$

So, probability (person drives an SUV ) $= \frac{39}{120}$

$= 0.325$

Part (b) - Step 1 : Given Information

We are given three different vehicles and if a person exercises or not . We need to find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.

Part (b) - Step 2 : Explanation

We need to add probability of both the cases .

Probability (person drives a sedan or exercises for at least 30 minutes four or more times per week) $=$ Probability (person drives a sedan) $+$ Probability (sedan in total ) $-$ Probability (yes in exercise)

Required probability $= \frac{45}{120} + \frac{52}{120} - \frac{25}{120} = \frac{72}{120} = 0.6$

Part (c) - Step 1 : Given Information

We are given different vehicles and if a person exercises or not. We need to find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week .