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) The empirical rule for the normal distribution states that approximately 95% of the data points lie within the range plus and minus 2 standard deviations of the population mean. Therefore one standard deviation can be found as follows:
\[\sigma=\frac{70-22}{4}=?\]
(b) Firstly find the z-score for 25 beats per minute as follows:
\[Z=\frac{25-45}{\sigma}=?\]
The use a standard normal distribution table to find the required probability.