https://file.aiquickdraw.com/mathbot/file/1728923720910w1r47omy.jpg

To solve part (b) of the problem based on the image, we need to calculate the standard deviation of the number of adults who have hypertension in a sample of 23 adults.

### Step 1: Identify the necessary data
- Proportion of adults with hypertension: \( p = 0.33 \) (or 33%)
- Sample size: \( n = 23 \)

### Step 2: Calculate the standard deviation
The formula for the standard deviation \( \sigma \) for a binomial distribution is:

\[
\sigma = \sqrt{n \cdot p \cdot (1 - p)}
\]

### Step 3: Substituting the values:
\[
\sigma = \sqrt{23 \cdot 0.33 \cdot (1 - 0.33)}
\]

\[
\sigma = \sqrt{23 \cdot 0.33 \cdot 0.67}
\]

\[
\sigma = \sqrt{5.0831}
\]

\[
\sigma \approx 2.2546
\]

### Final Answer:
The standard deviation of the number of adults who have hypertension is approximately **2.2546**.

Would you like further clarification or have any other questions?

### Related Questions:
1. How would the standard deviation change if the sample size increased?
2. What is the probability of exactly 7 adults in the sample having hypertension?
3. Can you explain how to interpret the mean and standard deviation in the context of this problem?
4. What assumptions are made when using the binomial distribution in this case?
5. How does the binomial distribution differ from other types of distributions?

### Tip:
The standard deviation measures how much the data varies from the mean, and a smaller value indicates that the data points are closer to the mean.

A national survey reported that 33% of adults in a certain country have hypertension. A sample of 23 adults is studied. What is the mean and standard deviation of the number of adults who have hypertension?

This problem explores how to calculate the mean and standard deviation for the number of adults with hypertension in a sample size of 23, using a 33% probability of hypertension based on national survey data. Learn how to apply binomial distribution formulas to solve statistical problems.

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