Suppose a geyser has a mean time between eruptions of 92 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes.Complete parts (a) through (e) below. Suppose a geyser has a mean time between eruptions of 92 minutes. Let the interval of time between the eruptions be normally distributed with standarddeviation 24 minutes. Complete parts (a) through (e) below.(a) What is the probability that a randomly selected time interval between eruptions is longer than 102 minutes?The probability that a randomly selected time interval is longer than 102 minutes is approximately(Round to four decimal places as needed.)(b) What is the probability that a random sample of 10 time intervals between eruptions has a mean longer than 102 minutes?The probability that the mean of a random sample of 10 time intervals is more than 102 minutes is approximately(Round to four decimal places as needed.)(c) What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 102 minutes?The probability that the mean of a random sample of 38 time intervals is more than 102 minutes is approximately(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 102 minutes, then the probability that the sample mean of the time between eruptions is greater than 102 minutesbecause the variability in the sample meanas the sample size(e) What might you conclude if a random sample of 38 time intervals between eruptions has a mean longer than 102 minutes? Select all that apply.O A. The population mean is 92, and this is an example of a typical sampling result.B. The population mean is 92, and this is just a rare sampling.C. The population mean may be greater than 92.D. The population mean cannot be 92, since the probability is so low.E. The population mean may be less than 92.F. The population mean must be less than 92, since the probability is so low.O G. The population mean must be more than 92, since the probability is so low.O O

(a) Obtain the probability that a randomly selected time interval between eruptions is longer…

Answered: Suppose a geyser has a mean time…

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Suppose a geyser has a mean time between eruptions of 92 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes.

Complete parts (a) through (e) below.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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