https://file.aiquickdraw.com/mathbot/file/1726543046018da9ju2jg.jpg

Let's analyze the problem step by step using the information from the image:

We are given:
- Lowest pulse rate = 37 beats per minute (bpm)
- Mean of pulse rates, \( \bar{x} = 76.0 \, \text{bpm} \)
- Standard deviation, \( s = 23.8 \, \text{bpm} \)

### Part (a):
**Find the difference between the pulse rate of 37 bpm and the mean pulse rate of 76.0 bpm.**

\[
\text{Difference} = 76.0 \, \text{bpm} - 37.0 \, \text{bpm}
\]

Let me calculate this difference.The difference between the pulse rate of 37 beats per minute and the mean pulse rate of 76.0 beats per minute is **39 beats per minute**.

### Part (b):
**How many standard deviations is the difference?**

We will use the formula for standard deviations:
\[
\text{Standard deviations} = \frac{\text{Difference}}{s}
\]
where \( s = 23.8 \, \text{bpm} \) is the standard deviation.

Let me calculate this next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually calculate the number of standard deviations by using the following formula:

\[
\text{Standard deviations} = \frac{\text{Difference}}{s} = \frac{39}{23.8} \approx 1.64
\]

This gives about **1.64 standard deviations**.

### Part (c):
**Convert the pulse rate of 37 bpm to a z-score.**

The formula for the z-score is:

\[
z = \frac{X - \bar{x}}{s}
\]

where:
- \( X = 37 \, \text{bpm} \) (the pulse rate we're converting)
- \( \bar{x} = 76.0 \, \text{bpm} \) (the mean pulse rate)
- \( s = 23.8 \, \text{bpm} \) (the standard deviation)

You can apply this formula using the given values.

### Part (d):
**Is the pulse rate of 37 bpm significantly low or high?**

Since z-scores between -2 and 2 are considered not significant, if the z-score of 37 bpm falls within this range, it is not significantly low or high.

Would you like any further details on these calculations?

Here are 5 related questions you could explore:
1. How do we interpret a z-score outside the range of -2 to 2?
2. What does it mean when the pulse rate is 1.64 standard deviations below the mean?
3. How would the interpretation change if the standard deviation were smaller?
4. What is the significance of a large standard deviation in biological data?
5. How would we use z-scores to compare different populations?

**Tip:** Z-scores are particularly useful for comparing values from different distributions, making it easier to understand how far a value is from the mean.

For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 37 beats per minute, the mean of the listed pulse rates is 76.0 beats per minute, and their standard deviation is 23.8 beats per minute.

This problem involves calculating the difference between a pulse rate of 37 beats per minute and the mean pulse rate of 76.0 bpm. It also includes the calculation of standard deviations and conversion of the pulse rate to a z-score. Suitable for Grades 10-12.

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