In a survey 200 people were polled at a local shopping center about spending free time playing sports, watching a movie, or reading a book. The relative frequency table below displays the results.
MOVIE SPORTS READ
MALE 0.25 0.30 0.10
FEMALE 0.15 0.05 0.15
a. How many males surveyed preferred playing sports?
b. How many people surveyed preferred to read a book?
c. How many females were surveyed?
a, .30 * 200 = ?
b. 200 ( 0.10 + 0.15) = ?
c. 200 ( 0.15 + 0.05 + 0.15) = ?
I'll be glad to check your answers.
To determine the answers to these questions, we need to refer to the relative frequency table. The table provides the relative frequencies of each activity preference for both males and females.
a. To find out how many males preferred playing sports, we need to look at the value in the "SPORTS" column under the "MALE" row. According to the table, the relative frequency for males playing sports is 0.30. To calculate the number of males surveyed who preferred playing sports, we multiply this relative frequency by the total number of people surveyed (200).
Number of males surveyed who preferred playing sports = 0.30 * 200 = 60
Therefore, 60 males surveyed preferred playing sports.
b. To determine the number of people surveyed who preferred reading a book, we need to sum up the relative frequencies from both males and females for the "READ" column.
Number of people surveyed who preferred reading a book = (Relative frequency for males reading) * 200 + (Relative frequency for females reading) * 200
= (0.10 * 200) + (0.15 * 200)
= 20 + 30
= 50
Therefore, 50 people surveyed preferred reading a book.
c. The table provides the relative frequencies of males and females, but it does not provide the actual count of males and females surveyed. To determine the number of females surveyed, we need to calculate the sum of the relative frequencies for females across all activities.
Number of females surveyed = (Relative frequency for females watching a movie) * 200 + (Relative frequency for females playing sports) * 200 + (Relative frequency for females reading) * 200
= (0.15 * 200) + (0.05 * 200) + (0.15 * 200)
= 30 + 10 + 30
= 70
Therefore, 70 females were surveyed.