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The problem you are working on is about calculating probabilities involving hypertension using binomial distribution.

Given:
- The probability \( p = 0.34 \) (since 34% of adults have hypertension).
- Sample size \( n = 24 \).

### Recap of Parts 1 and 2:

1. **Part (a):** The probability that exactly 4 people have hypertension is already solved as \( 0.0349 \).
   
2. **Part (b):** The probability that more than 8 people have hypertension is also provided as \( 0.4330 \).

### Let's solve **Part 3**:

**Part (c):** We need to calculate the probability that fewer than 4 people in the sample have hypertension.

This can be computed using the binomial probability formula:

\[
P(X < 4) = \sum_{x=0}^{3} \binom{n}{x} p^x (1-p)^{n-x}
\]

Where:
- \( n = 24 \) (sample size),
- \( p = 0.34 \) (probability of hypertension),
- \( X \) is the number of people with hypertension,
- We are summing the probabilities for \( X = 0 \), \( X = 1 \), \( X = 2 \), and \( X = 3 \).

You can use a binomial calculator or software to find these cumulative probabilities directly.

Would you like a more detailed explanation of the binomial calculation, or should I help you compute the value?

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Here are 5 related questions to consider:
1. How would the probability change if the sample size increased?
2. What is the expected number of people with hypertension in the sample?
3. How can we compute the standard deviation for this binomial distribution?
4. How would you calculate the probability for exactly 5 people having hypertension?
5. What would happen to the probabilities if the percentage of adults with hypertension increased to 40%?

**Tip:** The sum of probabilities for all possible outcomes in a binomial distribution must equal 1.

A national survey reported that 34% of adults in a certain country have hypertension. A sample of 24 adults is studied. (a) What is the probability that exactly 4 of them have hypertension? (b) What is the probability that more than 8 have hypertension? (c) What is the probability that fewer than 4 have hypertension?

Learn how to calculate probabilities related to hypertension in a sample of adults using the binomial distribution. This problem explores the likelihood of exact, more than, and fewer than certain numbers of cases, with a focus on binomial probabilities and cumulative calculations. Suitable for high school students.

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