Question

Estimating the Standard Deviation: Veterinary Science The resting heart rate
for an adult horse should average about 45 beats per minute with a (95% of
data) range from 22 to 70 beats per minute, based on information from The
Merck Veterinary Manual (a classic reference used in most veterinary colleges).
Let x be a random variable that represents the resting heart rate for an adult
horse. Assume that x has a distribution that is approximately normal.


(a) Estimate the standard deviation of the x distribution.

(b) What is the probability that the heart rate is less than 25 beats per minute?
(

Answer 1

(a) According to the empirical rule for a normal distribution approximately 95% of the data points lie within plus and minus two standard deviations from the mean.
In this case the range 22 to 70 beats per minute covers 4 standard deviations. Therefore one standard deviation is
\[\frac{70-22}{4}=\frac{48}{4}=?Beats\ per\ minute\]