To find the probability of a family having 4 members based on the given survey data, follow these steps:
1. Identify the family sizes and their corresponding frequencies:
- Family sizes: 2, 3, 4, 5, 6, 7, 8
- Frequencies: 87, 50, 61, 31, 16, 3, 2
2. Calculate the total number of families surveyed:
- Add up all the frequencies to get the total number of families.
[tex]\[
\text{Total number of families} = 87 + 50 + 61 + 31 + 16 + 3 + 2 = 250
\][/tex]
3. Find the frequency of families with 4 members:
- According to the given data, the frequency of families with 4 members is 61.
4. Calculate the probability of a family having 4 members:
- The probability [tex]\( P(4) \)[/tex] is given by the ratio of the frequency of families with 4 members to the total number of families.
[tex]\[
P(4) = \frac{\text{Frequency of families with 4 members}}{\text{Total number of families}}
\][/tex]
Substituting the numbers:
[tex]\[
P(4) = \frac{61}{250}
\][/tex]
5. Simplified probability:
- Divide 61 by 250 to get the probability in decimal form.
[tex]\[
P(4) = 0.244
\][/tex]
Therefore, the probability of picking a family with 4 members from the surveyed families is:
[tex]\[
P(4) = 0.244
\][/tex]
