In certain nerve cells, spontaneous electrical discharges are observed that are so rhythmically repetitive that they are called “clock spikes.” The timing of these spikes, even though remarkably regular, does exhibit variation. In one study, the interspike-time intervals (in milliseconds) for a single housefly (Musca domestica) were observed to follow a Normal distribution with mean 16.5 milliseconds and standard deviation 0.4 milliseconds. Let X= interspike-time interval for a randomly selected housefly. (a) What is the probability distribution of X? (b) Sketch the graph of the Normal distribution described in this problem. Clearly indicate on your sketch what the 68-95-99.7 rule predicts. (c) Using the 68-95-99.7 rule, compute P(X>17.3). Then give a practical interpretation of this probability.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In certain nerve cells, spontaneous electrical discharges are observed that are so rhythmically repetitive that they are called “clock spikes.” The timing of these spikes, even though remarkably regular, does exhibit variation. In one study, the interspike-time intervals (in milliseconds) for a single housefly (Musca domestica) were observed to follow a
Let X= interspike-time interval for a randomly selected housefly.
(a) What is the
(b) Sketch the graph of the Normal distribution described in this problem. Clearly indicate on your sketch what the
(c) Using the 68-95-99.7 rule, compute P(X>17.3). Then give a practical interpretation of this probability.
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