We are given the following information about the pulse rates of a sample of adult females:

• Lowest pulse rate: $39$ beats per minute
• Mean pulse rate: $\bar{x} = 71.0$ beats per minute
• Standard deviation: $s = 18.3$ beats per minute

(a) Difference between the pulse rate of 39 and the mean pulse rate

The difference is calculated as:

$\text{Difference} = \text{Mean} - \text{Lowest Pulse Rate}$

$= 71.0 - 39$

$= 32.0$

(b) How many standard deviations is this difference?

To determine how many standard deviations this difference represents, we divide it by the standard deviation:

$\text{Number of standard deviations} = \frac{\text{Difference}}{\text{Standard Deviation}}$

$= \frac{32.0}{18.3}$

$\approx 1.75$

(c) Convert the pulse rate of 39 beats per minute to a z-score

The z-score is calculated as:

$z = \frac{x - \bar{x}}{s}$

$= \frac{39 - 71.0}{18.3}$

$= \frac{-32.0}{18.3}$

$\approx -1.75$

(d) Is the pulse rate of 39 beats per minute significant?

A pulse rate is considered neither significantly low nor significantly high if its z-score is between -2 and 2.

Since the computed z-score is -1.75, it falls within this range. Therefore, the pulse rate of 39 beats per minute is not considered significantly low.

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Do you want further details or have any questions?

Related Questions:

1. What does a z-score represent in statistical terms?
2. How do we interpret a z-score of -1.75 in a real-world context?
3. If a pulse rate were 100 beats per minute, what would its z-score be?
4. What percentage of data falls within 1 standard deviation in a normal distribution?
5. How would the classification change if the threshold for significance was set at ±1.5 instead of ±2?

Tip:
A z-score tells us how far a data point is from the mean in terms of standard deviations. The farther from 0, the more unusual the value is!