Suppose a geyser has a mean time between eruptions of 70 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 17 minutes, answer the following question. (c) What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 78 minutes? The probability that the mean of a random sample of 30 time intervals is more than 78 minutes is approximately _____. (Round to four decimal places as needed.)
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!
Suppose a geyser has a
If the interval of time between the eruptions is
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