Let's break down the problem step by step.

We have the following dataLet's break down the problem step by step.

We have the following

• Lowest pulse rate: $36$ beats per minute
• Mean pulse rate $\overline{x} = 79.0$ beats per minute
• Standard deviation $s = 27.2$ beats per minute

Part a. Difference between the pulse rate of 36 and the mean pulse rate

The difference can be calculated as: $\text{Difference} = \overline{x} - 36$ Substitute the values: $\text{Difference} = 79.0 - 36 = 43.0$ So, the difference between the pulse rate of 36 beats per minute and the mean pulse rate is 43.0 beats per minute.

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Part b. How many standard deviations is the difference?

The number of standard deviations is found by dividing the difference by the standard deviation $s$: $\text{Number of standard deviations} = \frac{\text{Difference}}{s}$ Substitute the values: $\text{Number of standard deviations} = \frac{43.0}{27.2} \approx 1.58$ So, the difference is approximately 1.58 standard deviations.

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Part c. Convert the pulse rate of 36 beats per minute to a z-score

The formula for the z-score is: $z = \frac{x - \overline{x}}{s}$ where $x = 36$, $\overline{x} = 79.0$, and $s = 27.2$. Substitute the values: $z = \frac{36 - 79.0}{27.2} = \frac{-43.0}{27.2} \approx -1.58$ So, the z-score for a pulse rate of 36 beats per minute is approximately -1.58.

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Part d. Is the pulse rate of 36 significant?

We are given that pulse rates with z-scores between $-2$ and $2$ are considered neither significantly low nor high. Since the z-score for 36 beats per minute is $-1.58$, which lies between $-2$ and $2$, the pulse rate is not significant.

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Let me know if you need any further details!

Here are 5 related questions for deeper exploration:

1. What does a z-score represent in statistics, and why is it useful?
2. How would the interpretation change if the standard deviation were much smaller or larger?
3. What does it mean for a value to be "significantly low" in terms of z-scores?
4. How do outliers affect the mean and standard deviation of a data set?
5. Can we conclude anything about the distribution of pulse rates from this sample?

Tip: The z-score can help determine how far away a value is from the mean, making it a key tool for identifying outliers or significant values in a data set.