Question

1. a study of consumer smoking habits includes 198 people in the 18–22 age bracket (40 of whom smoke), 125 people in the 23–30 age bracket (31 of whom smoke), and 90 people in the 31–40 age bracket (30 of whom smoke). if one person is randomly selected from this sample, find the probability of getting someone who is age 23–30 or smokes.

a) 0.075 b) 0.248 c) 0.472 d) 0.547

1. a study of consumer smoking habits includes 186 people in the 18–22 age bracket (42 of whom smoke), 124 people in the 23–30 age bracket (40 of whom smoke), and 99 people in the 31–40 age bracket (21 of whom smoke). if one person is randomly selected from this sample, find the probability of getting someone who is age 18–22 or does not smoke.

a) 1.203 b) 0.851 c) 0.352 d) 0.774

1. the manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one monday. the frequency table below summarizes the results.

waiting time (minutes)	number of customers
4–7	10
8–11	12
12–15	4
16–19	4
20–23	2
24–27	2

if we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes?
a) 0.093 b) 0.651 c) 0.558 d) 0.727

Explanation:

Question 4

Step1: Find total number of people

Total = 198 + 125 + 90 = 413

Step2: Find number of people in 23 - 30 or smoke

Let \( A \) be age 23 - 30, \( B \) be smoke.
\( n(A) = 125 \), \( n(B) = 40 + 31 + 30 = 101 \), \( n(A\cap B) = 31 \)
Using formula \( n(A\cup B)=n(A)+n(B)-n(A\cap B) \)
\( n(A\cup B)=125 + 101 - 31 = 195 \)

Step3: Calculate probability

Probability = \( \frac{195}{413} \approx 0.472 \)

Step1: Find total number of people

Total = 186 + 124 + 99 = 409

Step2: Find number of people who smoke

Smokers = 42 + 40 + 21 = 103, so non - smokers = 409 - 103 = 306

Step3: Find number of people in 18 - 22 or non - smoke

Let \( A \) be age 18 - 22, \( B \) be non - smoke.
\( n(A)=186 \), \( n(B) = 306 \), \( n(A\cap B)=186 - 42=144 \)
Using formula \( n(A\cup B)=n(A)+n(B)-n(A\cap B) \)
\( n(A\cup B)=186+306 - 144 = 348 \)

Step4: Calculate probability

Probability=\( \frac{348}{409}\approx0.851 \)

Step1: Find total number of customers

Total = 9+10 + 12+4+4+2+2=43

Step2: Define events

Let \( A \): waiting time at least 12 minutes (12 - 15, 16 - 19, 20 - 23, 24 - 27), \( n(A)=4 + 4+2+2 = 12 \)
Let \( B \): waiting time between 8 and 15 minutes (8 - 11, 12 - 15), \( n(B)=12 + 4=16 \)
\( A\cap B \): waiting time between 12 and 15 minutes, \( n(A\cap B) = 4 \)

Step3: Use union formula

\( n(A\cup B)=n(A)+n(B)-n(A\cap B)=12 + 16-4 = 24 \)

Step4: Calculate probability

Probability=\( \frac{24}{43}\approx0.558 \)

Answer:

C) 0.472

Question 5