The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minutes, complete parts (a) through (f). (a) What is the probability that a randomly selected time interval between eruptions is longer than 94 minutes? The probability that a randomly selected time interval is longer than 94 minutes is approximately 0.3372. (Round to four decimal places as needed.) (b) What is the probability that random sample of 10 time intervals between eruptions has a mean longer than 94 minutes? The probability that the mean of a random sample of 10 time intervals is more than 94 minutes is approximately 0.0901. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 33 time intervals between eruptions has a mean longer than 94 minutes? The probability that the mean of a random sample of 33 time intervals is more than 94 minutes is approximately 0.0075. (Round to four decimal places as needed.) (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 94 minutes, then the probability that the sample mean of the time between eruptions is greater than 94 minutes V because the variability in the sample mean as the sample size

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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!