Concept explainers
Emergency Room Traffic. A variable is said to have an exponential distribution or to be exponentially distributed if its distribution has the shape of an exponential curve, that is, a curve of the form y = e−x/μ/μ for x > 0, where μ is the
- a. Sketch the exponential curve for the distribution of the variable “interarrival time.” Note that this variable is far from being
normally distributed. What shape does its distribution have? - b. Use the technology of your choice to simulate 1000 samples of four interarrival times each.
- c. Find the sample mean of each of the 1000 samples.
- d. Determine the mean and standard deviation of the 1000 sample means.
- e. Theoretically, what are the mean and the standard deviation of all possible sample means for samples of size 4? Compare your answers to those you obtained in part (d).
- f. Obtain a histogram of the 1000 sample means. Is the histogram bell shaped? Would you necessarily expect it to be?
- g. Repeat parts (b)–(f) for a
sample size of 40.
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