suppose that resting pulse rates among healthy adults are normally distributed with a mean of 73 beats per minute and a standard deviation of 20 beats per minute. Find the percentage of adults who have resting pulse rates that are less than 98 beats per minute.

To find the percentage of adults with resting pulse rates less than 98 beats per minute, we need to calculate the probability that a normally distributed random variable with a mean of 73 beats per minute and a standard deviation of 20 beats per minute is less than 98 beats per minute.

### Step 1: Standardize the value
We first convert the value 98 beats per minute into a z-score using the formula:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- \( X = 98 \) (the value we're interested in)
- \( \mu = 73 \) (the mean)
- \( \sigma = 20 \) (the standard deviation)

\[
z = \frac{98 - 73}{20} = \frac{25}{20} = 1.25
\]

### Step 2: Find the probability associated with the z-score
Next, we look up the z-score of 1.25 in the standard normal distribution table, or use a calculator.

The probability corresponding to a z-score of 1.25 is approximately 0.8944. This means that about 89.44% of the data falls below a z-score of 1.25.

### Conclusion:
Thus, approximately **89.44%** of adults have resting pulse rates that are less than 98 beats per minute.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. What is the percentage of adults with a resting pulse rate higher than 98 beats per minute?
2. How would the percentage change if the standard deviation was 15 instead of 20?
3. What is the z-score for a pulse rate of 60 beats per minute?
4. How can we find the pulse rate that corresponds to the top 10% of this distribution?
5. How would you calculate the percentage for a range of pulse rates, say between 60 and 80 beats per minute?

**Tip:** Understanding the concept of z-scores is key when working with normally distributed data, as they allow you to standardize different data points and compare them directly.

Learn how to calculate the percentage of adults with resting pulse rates less than 98 beats per minute using the normal distribution and z-score formula. Understand the concept of standardizing data points and interpreting probabilities in a normal distribution. Suitable for advanced high school students and anyone interested in statistics and probability.

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