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This problem involves a normal distribution of pulse rates among healthy adults, with a mean (\(\mu\)) of 80 beats per minute and a standard deviation (\(\sigma\)) of 10 beats per minute. We are asked to find the proportion of healthy adults with pulse rates greater than 91 beats per minute.

### Steps to Solve:

1. **Convert the raw score (91) to a z-score** using the formula:
   \[
   z = \frac{X - \mu}{\sigma}
   \]
   where \(X = 91\), \(\mu = 80\), and \(\sigma = 10\).

   \[
   z = \frac{91 - 80}{10} = \frac{11}{10} = 1.1
   \]

2. **Find the area to the right of \(z = 1.1\)**:
   - Using standard normal distribution tables or a calculator, we find that the cumulative probability up to \(z = 1.1\) is approximately 0.8643.
   - The proportion greater than 91 beats per minute is the area to the right of this z-score, so:
     \[
     P(X > 91) = 1 - 0.8643 = 0.1357
     \]

Thus, the proportion of healthy adults with pulse rates greater than 91 beats per minute is approximately **0.1357** (rounded to four decimal places).

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### Related Questions:
1. How do you calculate the z-score for values below the mean?
2. What is the probability that a pulse rate is less than 75 beats per minute?
3. How do you use a z-score table to find probabilities?
4. What is the proportion of adults with pulse rates between 70 and 90 beats per minute?
5. How would the answer change if the standard deviation were smaller, say 5 beats per minute?

### Tip:
Always check the area under the normal curve when calculating probabilities, and remember that the total area equals 1.

Suppose that pulse rates among healthy adults are normally distributed with a mean of 80 beats per minute and a standard deviation of 10 beats per minute. What proportion of healthy adults have pulse rates that are more than 91 beats per minute? Round your answer to at least four decimal places.

Learn how to calculate the proportion of healthy adults with pulse rates greater than 91 beats per minute. The problem involves a normal distribution with a mean of 80 bpm and a standard deviation of 10 bpm. Find out how to convert raw scores to z-scores and determine probabilities. Suitable for students in Grades 10-12.

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