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1.   Has the percentage of young girls drinking milk changed over time?  The following table is consistent with the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (by Shanthy A. Bowman)



 
(a)   What percent of the young girls drink milk?

(b)   What percent of the young girls were in the 1989-1991 survey?

(c)   What percent of the young girls reported that they drink milk were surveyed in 1989- 1991?

(d)   What percent of the young girls in 1989-1991 drink milk?

(e)   What is the marginal distribution of milk consumption?

Let's address the questions based on the table provided:

### (a) What percent of the young girls drink milk?

To find this percentage, we need the total number of girls who drink milk out of the total number of girls surveyed. From the table:

- Total number of girls who drink milk = 1222 (sum of "Yes" column under "Drinks Fluid Milk").
- Total number of girls surveyed = 2149 (the grand total at the bottom right of the table).

The percentage is calculated as:

\[
\text{Percentage} = \left(\frac{1222}{2149}\right) \times 100 \approx 56.85\%
\]

So, **56.85%** of the young girls drink milk.

---

### (b) What percent of the young girls were in the 1989-1991 survey?

To find this percentage, we use the total number of girls surveyed in 1989-1991, which is 837 (the second column total).

The percentage is calculated as:

\[
\text{Percentage} = \left(\frac{837}{2149}\right) \times 100 \approx 38.95\%
\]

So, **38.95%** of the young girls were surveyed in 1989-1991.

---

### (c) What percent of the young girls reported that they drink milk were surveyed in 1989-1991?

To find this percentage, we take the number of girls who reported drinking milk in 1989-1991, which is 502 (from the "Yes" row in the 1989-1991 column), and divide it by the total number of girls who drink milk, which is 1222.

\[
\text{Percentage} = \left(\frac{502}{1222}\right) \times 100 \approx 41.08\%
\]

So, **41.08%** of the young girls who drink milk were surveyed in 1989-1991.

---

### (d) What percent of the young girls in 1989-1991 drink milk?

To find this percentage, we take the number of girls who drink milk in 1989-1991 (502) and divide it by the total number of girls surveyed in 1989-1991 (837).

\[
\text{Percentage} = \left(\frac{502}{837}\right) \times 100 \approx 59.98\%
\]

So, **59.98%** of the young girls in 1989-1991 drink milk.

---

### (e) What is the marginal distribution of milk consumption?

The marginal distribution of milk consumption describes the proportion of girls who drink milk (Yes) and do not drink milk (No) in relation to the total number of girls surveyed.

- Number of girls who drink milk (Yes): 1222.
- Number of girls who do not drink milk (No): 927.
- Total number of girls surveyed: 2149.

The marginal distribution is:

\[
\text{Yes: } \frac{1222}{2149} \times 100 \approx 56.85\% \quad (\text{drink milk})
\]
\[
\text{No: } \frac{927}{2149} \times 100 \approx 43.15\% \quad (\text{do not drink milk})
\]

Thus, the marginal distribution is:
- **56.85% drink milk**
- **43.15% do not drink milk**

---

Would you like more details on any of these calculations or a deeper explanation of marginal distributions? 

### Here are 5 related questions to further explore:
1. How has the percentage of young girls drinking milk changed between 1987-1988 and 1994-1996?
2. What is the total number of girls who drank milk in the 1994-1996 survey?
3. What is the conditional probability that a girl drinks milk given that she was surveyed in 1994-1996?
4. What is the trend in the percentage of girls who do not drink milk across the surveys?
5. How does the total number of girls who do not drink milk compare between the different survey periods?

### Tip:
When analyzing a table, it's useful to compute both percentages within categories (conditional percentages) and marginal distributions to get a fuller understanding of the data!

Has the percentage of young girls drinking milk changed over time?

Explore the changes in milk consumption among young girls from 1987 to 1996. This analysis uses percentage calculations to show trends over three survey periods, providing insights into dietary shifts.

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