A survey of 1000 television viewers conducted by a local television station produced the following data:
•40% watch the news at 12:00
•60% watch the news at 18:00
•50% watch the news at 23:00
•25% watch the news at 12:00 and at 18:00
•20% watch the news at 18:00 and at 23:00
•10% watch all three news broadcasts
a) what percentages of those surveyed watch at least one of these programs?
b)what percent watch none of these broadcasts?
c) what percent view the news at 12:00 and at 18:00,but not at 23:00
e)What percent watches exactly two of these shows.
a) To find the percentage of those surveyed who watch at least one of these programs, we need to add the percentages of people who watch each individual program and subtract the percentages of people who watch multiple programs more than once.
- Percentage who watch the news at 12:00 = 40%
- Percentage who watch the news at 18:00 = 60%
- Percentage who watch the news at 23:00 = 50%
To avoid double-counting, we subtract the percentages of people who watch multiple programs more than once:
- Percentage who watch at 12:00 and at 18:00 = 25%
- Percentage who watch at 18:00 and at 23:00 = 20%
- Percentage who watch all three news broadcasts = 10%
Calculating:
Percentage who watch at least one of these programs = Percentage who watch news at 12:00 + Percentage who watch news at 18:00 + Percentage who watch news at 23:00 - Percentage who watch at 12:00 and 18:00 - Percentage who watch at 18:00 and 23:00 + Percentage who watch all three news broadcasts
= 40% + 60% + 50% - 25% - 20% + 10%
= 115%
Therefore, 115% of those surveyed watch at least one of these programs.
b) To find the percentage who watch none of these broadcasts, we subtract the percentage who watch at least one program (which we found in part a) from 100%.
Percentage who watch none of these broadcasts = 100% - Percentage who watch at least one of these programs
= 100% - 115%
= -15%
It is not possible to have a negative percentage, so there might be an error in the given data or calculations provided. Please double-check the provided information or perform additional calculations to clarify the answer.
c) To find the percentage who view the news at 12:00 and at 18:00 but not at 23:00, we need to subtract the percentages of people who watch the news broadcasts at all three time slots.
Percentage who view the news at 12:00 and at 18:00, but not at 23:00 = Percentage who watch at 12:00 and at 18:00 - Percentage who watch all three news broadcasts
= 25% - 10%
= 15%
Therefore, 15% of those surveyed view the news at 12:00 and at 18:00 but not at 23:00.
d) To find the percentage who watch exactly two of these shows, we need to subtract the percentages of people who watch all three news broadcasts from the total percentage who watch at least two programs.
Percentage who watch exactly two of these shows = Percentage who watch at least two programs - Percentage who watch all three news broadcasts
= (Percentage who watch at 12:00 and at 18:00 + Percentage who watch at 18:00 and at 23:00 + Percentage who watch at 12:00 and at 23:00) - Percentage who watch all three news broadcasts
= (25% + 20% + ???) - 10%
= ???
Unfortunately, we do not have enough information to calculate the exact percentage in this case.
To find the percentages of those surveyed who watch at least one of the programs, we need to add up the percentages of people who watch each program individually and subtract the overlap percentages.
a) Find the percentage of people who watch at least one of the programs:
Percentage of people who watch the news at 12:00 = 40%
Percentage of people who watch the news at 18:00 = 60%
Percentage of people who watch the news at 23:00 = 50%
Now, we need to subtract the overlaps:
Percentage of people who watch the news at both 12:00 and 18:00 = 25%
Percentage of people who watch the news at both 18:00 and 23:00 = 20%
Percentage of people who watch all three news broadcasts = 10%
Calculating the percentage of people who watch at least one of the programs:
40% + 60% + 50% - 25% - 20% - 10% = 95%
Therefore, 95% of those surveyed watch at least one of the programs.
b) To find the percentage of people who watch none of these broadcasts, subtract the percentage of people who watch at least one of the programs from 100%:
100% - 95% = 5%
Therefore, 5% of those surveyed watch none of these broadcasts.
c) To find the percentage of people who view the news at 12:00 and at 18:00 but not at 23:00, we need to subtract the overlapping percentages.
Percentage of people who watch the news at both 12:00 and 18:00 = 25%
Percentage of people who watch all three news broadcasts = 10%
Calculating the percentage who watch at 12:00 and 18:00 but not at 23:00:
25% - 10% = 15%
Therefore, 15% of those surveyed view the news at 12:00 and 18:00 but not at 23:00.
d) To find the percentage of people who watch exactly two of these shows, we need to add up the overlapping percentages without including the percentage of people who watch all three news broadcasts.
Percentage of people who watch the news at both 12:00 and 18:00 = 25%
Percentage of people who watch the news at both 18:00 and 23:00 = 20%
Percentage of people who watch all three news broadcasts = 10%
Calculating the percentage of people who watch exactly two of these shows:
25% + 20% - 10% = 35%
Therefore, 35% of those surveyed watch exactly two of these shows.