Question

For a physiology class experiment, a student is fitted with a lightweight waterproof device that measures her average pulse rate over 2-hourly intervals. Consider 12 consecutive intervals over a 24-hour period, and let X be the number of these intervals in which the average pulse rate is less than 100 beats per minute. Is it reasonable to treat X as an observation from a binomial distribution? Justify your answer.

Answer 1

For a binomial distribution, below conditions needs to be satisfied.

• The experiment consists of n repeated trials. In the problem, the experiment consists of 12 repeated trials.
• Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. In the problem, each trial result in just two possible outcomes - average pulse rate is less than 100 beats per minute (success) and average pulse rate is greater than or equal to 100 beats per minute (failure)
• The probability of success, denoted by P, is the same on every trial. In the problem, we cannot assume that the probability of average pulse rate less than 100 beats per minute is not same on every trial.
• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials. In the problem, we cannot assume that the outcome on one trial does not affect the outcome on other trials. A high pulse rate in a given interval may also cause high pulse rate in consecutive intervals.

Thus, all conditions of binomial distribution are not satisfied. It is not reasonable to treat X as an observation from a binomial distribution