Select the correct answer.
An investment banking house conducted a survey to determine how two of its proposed investment plans for three different age categories are used. This table shows the responses they received.
Plan I Plan II Neither
Ages 26–35 19 14 17
Ages 36–45 14 28 8
Ages 46–55 27 21 2
What percentage of people preferring plan I are from the 36–45 age group, and what percentage of people from the 46–55 age group prefer plan II? Round your answers to the nearest whole number.
A.
23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
B.
28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
C.
23% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II.
D.
28% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II.
E.
32% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
Option B: 28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
To find the percentage of people preferring plan I from the 36-45 age group, we need to divide the number of responses for Plan I in that group by the total number of responses in that group, and then multiply by 100. So, for ages 36-45:
Percentage of people preferring Plan I = (14 / (14 + 28 + 8)) x 100 = 28%
To find the percentage of people from the 46-55 age group who prefer Plan II, we need to divide the number of responses for Plan II in that group by the total number of responses in that group, and then multiply by 100. So, for ages 46-55:
Percentage of people preferring Plan II = (21 / (27 + 21 + 2)) x 100 = 42%
Rounding these answers to the nearest whole number gives us option B.
To find the percentage of people preferring plan I from the 36–45 age group, we need to divide the number of people preferring plan I in that age group by the total number of people preferring plan I.
For the 36–45 age group, the number of people preferring plan I is given as 14.
The total number of people preferring plan I is calculated by adding the number of people preferring plan I in each age group:
Total number of people preferring plan I = 19 (Ages 26–35) + 14 (Ages 36–45) + 27 (Ages 46–55) = 60.
The percentage of people preferring plan I from the 36–45 age group is therefore (14/60) * 100 = 23%.
To find the percentage of people from the 46–55 age group who prefer plan II, we need to divide the number of people preferring plan II in that age group by the total number of people from the 46–55 age group.
For the 46–55 age group, the number of people preferring plan II is given as 21.
The total number of people from the 46–55 age group is calculated by adding the number of people preferring each plan in that age group:
Total number of people from the 46–55 age group = 27 (Plan I) + 21 (Plan II) + 2 (Neither) = 50.
The percentage of people from the 46–55 age group who prefer plan II is therefore (21/50) * 100 = 42%.
Therefore, the correct answer is:
A. 23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.