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Nov 2015 p61 q4
3144
Amy’s friend Marok measured her pulse rate every day after running for half an hour. Marok’s pulse rate, in beats per minute, was found to have a mean of 148.6 and a standard deviation of 18.5. Assuming that pulse rates have a normal distribution, find what proportion of Marok’s pulse rates, after running for half an hour, were above 160 beats per minute.
Solution
To find the proportion of Marok’s pulse rates above 160 beats per minute, we standardize the value using the formula for the z-score:
\(z = \frac{X - \mu}{\sigma}\)
where \(X = 160\), \(\mu = 148.6\), and \(\sigma = 18.5\).
\(z = \frac{160 - 148.6}{18.5} = 0.616\)
We need to find \(P(X > 160) = P(z > 0.616)\).
Using the standard normal distribution table, \(P(z > 0.616) = 1 - P(z < 0.616) = 1 - 0.7310 = 0.269\).
Thus, the proportion of pulse rates above 160 beats per minute is 0.269.