Question
How many kids? In a survey 46122 women were asked how many children they had. The results were as follows.
Number of Children Number of Women
0: 12520
1: 7465
2: 11297
3: 7024
4: 3779
5: 1816
6: 922
7: 526
8 or more 773
Total 46122
(c) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than seven children. Round your answer to four decimal places.
Number of Children Number of Women
0: 12520
1: 7465
2: 11297
3: 7024
4: 3779
5: 1816
6: 922
7: 526
8 or more 773
Total 46122
(c) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than seven children. Round your answer to four decimal places.
Answers
GPT-4o mini
To estimate the probability that a woman has more than seven children using the empirical method, we need to calculate the total number of women who have more than seven children and then divide that by the total number of women surveyed.
From the data provided, we have:
- Number of women with 8 or more children: **773**
Total number of women surveyed: **46122**
Now, we can calculate the probability \( P(X > 7) \):
\[
P(X > 7) = \frac{\text{Number of women with more than 7 children}}{\text{Total number of women}} = \frac{773}{46122}
\]
Calculating this gives:
\[
P(X > 7) = \frac{773}{46122} \approx 0.0167
\]
Rounding to four decimal places, the probability that a woman has more than seven children is:
\[
\boxed{0.0168}
\]
From the data provided, we have:
- Number of women with 8 or more children: **773**
Total number of women surveyed: **46122**
Now, we can calculate the probability \( P(X > 7) \):
\[
P(X > 7) = \frac{\text{Number of women with more than 7 children}}{\text{Total number of women}} = \frac{773}{46122}
\]
Calculating this gives:
\[
P(X > 7) = \frac{773}{46122} \approx 0.0167
\]
Rounding to four decimal places, the probability that a woman has more than seven children is:
\[
\boxed{0.0168}
\]
apparently this is incorrect
GPT-4o mini
Let’s go through the calculations step by step to ensure accuracy.
We need to calculate the probability of a woman having more than 7 children, which includes those who have 8 or more children based on the survey data provided.
From the data:
- Number of women with **8 or more** children: **773**
To find the probability that a woman has more than 7 children, we will use the total number of surveyed women, which is 46122.
The probability \( P(X > 7) \) is calculated as:
\[
P(X > 7) = \frac{\text{Number of women with more than 7 children}}{\text{Total number of women}}
\]
Substituting the known values:
\[
P(X > 7) = \frac{773}{46122}
\]
Now, let’s calculate the probability:
\[
P(X > 7) \approx \frac{773}{46122} \approx 0.0167
\]
Calculating this value precisely:
1. **773 divided by 46122**:
\[
\frac{773}{46122} \approx 0.01675
\]
Rounding this value to four decimal places gives:
\[
0.0168
\]
Thus, I see that the original assessment aligns with this recalculation.
Therefore, the probability that a woman has more than seven children is indeed:
\[
\boxed{0.0168}
\]
If there is a specific reason you believe this answer to be incorrect, please provide additional context, and I will be glad to help resolve any discrepancies.
We need to calculate the probability of a woman having more than 7 children, which includes those who have 8 or more children based on the survey data provided.
From the data:
- Number of women with **8 or more** children: **773**
To find the probability that a woman has more than 7 children, we will use the total number of surveyed women, which is 46122.
The probability \( P(X > 7) \) is calculated as:
\[
P(X > 7) = \frac{\text{Number of women with more than 7 children}}{\text{Total number of women}}
\]
Substituting the known values:
\[
P(X > 7) = \frac{773}{46122}
\]
Now, let’s calculate the probability:
\[
P(X > 7) \approx \frac{773}{46122} \approx 0.0167
\]
Calculating this value precisely:
1. **773 divided by 46122**:
\[
\frac{773}{46122} \approx 0.01675
\]
Rounding this value to four decimal places gives:
\[
0.0168
\]
Thus, I see that the original assessment aligns with this recalculation.
Therefore, the probability that a woman has more than seven children is indeed:
\[
\boxed{0.0168}
\]
If there is a specific reason you believe this answer to be incorrect, please provide additional context, and I will be glad to help resolve any discrepancies.
(d) Using a cutoff of , 0.05 is it unusual for a woman to have no children?
GPT-4o mini
To determine whether it is unusual for a woman to have no children using a cutoff of 0.05, we need to calculate the empirical probability of a woman having no children and compare it to the cutoff.
From the data provided, the number of women who have **0 children** is **12,520**, and the total number of women surveyed is **46,122**.
The probability \( P(X = 0) \) that a woman has no children is calculated as follows:
\[
P(X = 0) = \frac{\text{Number of women with 0 children}}{\text{Total number of women}} = \frac{12520}{46122}
\]
Calculating this probability:
\[
P(X = 0) \approx \frac{12520}{46122} \approx 0.2715
\]
Now, we compare this probability to the cutoff of **0.05**:
- If \( P(X = 0) < 0.05 \), then it would be considered unusual.
- If \( P(X = 0) \geq 0.05 \), then it would not be considered unusual.
Since \( 0.2715 > 0.05 \), it is **not unusual** for a woman to have no children based on the empirical data from this survey.
Therefore, the conclusion is:
**It is not unusual for a woman to have no children.**
From the data provided, the number of women who have **0 children** is **12,520**, and the total number of women surveyed is **46,122**.
The probability \( P(X = 0) \) that a woman has no children is calculated as follows:
\[
P(X = 0) = \frac{\text{Number of women with 0 children}}{\text{Total number of women}} = \frac{12520}{46122}
\]
Calculating this probability:
\[
P(X = 0) \approx \frac{12520}{46122} \approx 0.2715
\]
Now, we compare this probability to the cutoff of **0.05**:
- If \( P(X = 0) < 0.05 \), then it would be considered unusual.
- If \( P(X = 0) \geq 0.05 \), then it would not be considered unusual.
Since \( 0.2715 > 0.05 \), it is **not unusual** for a woman to have no children based on the empirical data from this survey.
Therefore, the conclusion is:
**It is not unusual for a woman to have no children.**