What's a normal pulse rate? That depends on a variety of...

What's a normal pulse rate? That depends on a variety of factors. Pulse rates between 60 and 100 beats per minute are considered normal for children over 10 and adults. ${ }^{8}$ Suppose that these pulse rates are approximately normally distributed with a mean of 78 and a standard deviation of 12 . a. What proportion of adults will have pulse rates between 60 and $100 ?$ b. What is the 95 th percentile for the pulse rates of adults? c. Would a pulse rate of 110 be considered unusual? Explain.

What's a normal pulse rate? That depends on a variety of factors. Pulse rates between 60 and 100 beats per minute are considered normal for children over 10 and adults. ${ }^{8}$ Suppose that these pulse rates are approximately normally distributed with a mean of 78 and a standard deviation of 12 .
a. What proportion of adults will have pulse rates between 60 and $100 ?$
b. What is the 95 th percentile for the pulse rates of adults?
c. Would a pulse rate of 110 be considered unusual? Explain.

Key Concepts

Probability Calculations

Probability calculations in a normal distribution involve determining the area under the curve between specified values. This area represents the likelihood or proportion of observations falling within that interval.

Identification of Unusual Values

In the context of the normal distribution, unusual values are often identified as those that lie more than 2 or 3 standard deviations away from the mean. Such values are considered outliers or rare occurrences within the distribution.

Percentiles

Percentiles are values below which a certain percentage of observations in a distribution fall. In the context of a normal distribution, percentiles help identify thresholds, such as the 95th percentile, which represents the point below which 95% of the data lies.

Mean and Standard Deviation

The mean is the arithmetic average of a distribution and serves as the center of the data, while the standard deviation measures the spread or variability of the distribution around the mean. In a normal distribution, these two parameters fully describe the shape and location of the curve.

Normal Distribution

A normal distribution is a continuous probability distribution that is symmetric about its mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve and is widely used in statistics because many natural phenomena exhibit this type of distribution.

Z-Score Transformation

A z-score is a standardized score that indicates how many standard deviations an element is from the mean. By transforming raw values into z-scores, one can use standard normal distribution tables or software to compute probabilities and percentiles regardless of the original scale of the data.

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