Question

A certain group of test subjects had pulse rates with a mean of 75.2 beats per minute and a standard deviation of 11.2 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 147.6 beats per minute significantly low or significantly​ high?

Answer 1

The z-score for a pulse rate of 147.6 beats per minute is 6.46 > 2, which means that this pulse rate is significantly high.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

By the Range Rule of Thumb, if Z < -2, the measure X is significantly low, and if Z > 2, the measure X is significantly high.

Mean of 75.2 beats per minute and a standard deviation of 11.2 beats per minute.

This means that
`\mu = 75.2, \sigma = 11.2`

Is a pulse rate of 147.6 beats per minute significantly low or significantly​ high?

We have to find Z when X = 147.6. So

`Z = (X - \mu)/(\sigma)`

`Z = (147.6 - 75.2)/(11.2)`

`Z = 6.46`

The z-score for a pulse rate of 147.6 beats per minute is 6.46 > 2, which means that this pulse rate is significantly high.