Question

The following data are the lengths of time (in minutes) between eruptions for a sample of eruptions of the Old Faithful geyser in Yellowstone National Park. 83 76 86 82 87

a. Calculate the mean, variance, and standard deviation for the data. Be sure to follow the rounding conventions and include the correct units!

X = _____ s² = _____ s = _____

b. Based on the mean and standard deviation, would 90 minutes be considered significantly high? Justify your answer.

Answer 1

tabulating the values,we get

sample mean = 82.8 minutes

sample variance = 18.7 minutes

sample standard deviation = 4.324 minutes

mean + 2xs = 82.8+2x4.324 = 91.448

if we assume the populaton to be normally distrbuted then, as per empirical rule, almost 95% of data value lie within 2 standard deviations from mean.

since, 90 lies within 2 standard deviaton from mean so, its not significantly higher and well wthin the usual range.