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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? (
(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.