The 2015 National Vital Statistics Report provides information on how the nearly four million live births that occurred in 2014 broke down by birth order. Choose at random a baby born in the United States in 2014. Baby's birth order Probability mean = 1 2 0.391 0.319 The few babies who were 9th or more in birth order are included in the "8" birth order group. In 2014, 39.1% of the nearly 4 million live births in the United States were to first-time mothers. 3 5 6 7 4 0.168 0.072 0.028 0.012 0.005 standard deviation = What are the properties of the sampling distribution of the proportion of births to first-time mothers in random samples of 500 births from 2014? (Enter your answer for the mean rounded to three decimal place and your answer for the standard deviation rounded to four decimal places.) 8 0.005

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**Title: Birth Order Probability and Sampling Distribution in the United States (2014)**

**Introduction:**
The 2015 National Vital Statistics Report provides insights into how nearly four million live births in the United States in 2014 were distributed across different birth orders. An analysis of these statistics can provide a better understanding of birth patterns during this period.

**Birth Order Probability Table:**

| Baby's Birth Order | 1    | 2    | 3    | 4    | 5    | 6    | 7    | 8+   |
|--------------------|------|------|------|------|------|------|------|------|
| Probability        | 0.391| 0.319| 0.168| 0.072| 0.028| 0.012| 0.005| 0.005|

**Interpretation:**
- The table presents the probability of a randomly chosen baby being of a particular birth order.
- Babies who are 9th or more in birth order are included in the "8" category.

**Key Insight:**
In 2014, 39.1% of the nearly four million live births in the United States were to first-time mothers.

**Sampling Distribution:**
The question examines the properties of the sampling distribution of the proportion of births to first-time mothers in random samples of 500 births from 2014.

**Calculation Objectives:**
- Determine the mean of the sampling distribution, rounded to three decimal places.
- Calculate the standard deviation of the sampling distribution, rounded to four decimal places.

**Conclusion:**
Understanding these probabilities and the subsequent sampling distributions can yield valuable insights into family planning and demographic trends in the United States. These statistics are vital for researchers, policymakers, and educators focusing on population studies and maternal health.
Transcribed Image Text:**Title: Birth Order Probability and Sampling Distribution in the United States (2014)** **Introduction:** The 2015 National Vital Statistics Report provides insights into how nearly four million live births in the United States in 2014 were distributed across different birth orders. An analysis of these statistics can provide a better understanding of birth patterns during this period. **Birth Order Probability Table:** | Baby's Birth Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8+ | |--------------------|------|------|------|------|------|------|------|------| | Probability | 0.391| 0.319| 0.168| 0.072| 0.028| 0.012| 0.005| 0.005| **Interpretation:** - The table presents the probability of a randomly chosen baby being of a particular birth order. - Babies who are 9th or more in birth order are included in the "8" category. **Key Insight:** In 2014, 39.1% of the nearly four million live births in the United States were to first-time mothers. **Sampling Distribution:** The question examines the properties of the sampling distribution of the proportion of births to first-time mothers in random samples of 500 births from 2014. **Calculation Objectives:** - Determine the mean of the sampling distribution, rounded to three decimal places. - Calculate the standard deviation of the sampling distribution, rounded to four decimal places. **Conclusion:** Understanding these probabilities and the subsequent sampling distributions can yield valuable insights into family planning and demographic trends in the United States. These statistics are vital for researchers, policymakers, and educators focusing on population studies and maternal health.
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