Question
A field of geysers in Yellowstone may display an eruption between once every 45 minutes, to as much as every 13 hours. Assume the probability is a uniform continuous probability distribution. Find the theoretical average time between eruptions for geysers in this field, and the theoretical standard deviation for these times.
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Answer to a math question A field of geysers in Yellowstone may display an eruption between once every 45 minutes, to as much as every 13 hours. Assume the probability is a uniform continuous probability distribution. Find the theoretical average time between eruptions for geysers in this field, and the theoretical standard deviation for these times.
Cristian
4.7111 Answers
1. The eruption times are uniformly distributed between 45 minutes and 13 hours.
2. Convert 45 minutes to hours:45 \text{ minutes} = \frac{45}{60} = 0.75 \text{ hours}
3. The random variableX [0.75, 13]
4. The average (mean) of a uniform distributiona b \frac{a + b}{2}
\text{Mean} = \frac{0.75 + 13}{2} = \frac{13.75}{2} = 6.875
5. The standard deviation of a uniform distribution froma b \frac{b-a}{\sqrt{12}}
\text{Standard Deviation} = \frac{13 - 0.75}{\sqrt{12}} = \frac{12.25}{\sqrt{12}} = \frac{12.25}{3.464} \approx 3.5367
Therefore, the mean eruption time is6.875 \text{ hours} 3.5367 \text{ hours}
2. Convert 45 minutes to hours:
3. The random variable
4. The average (mean) of a uniform distribution
5. The standard deviation of a uniform distribution from
Therefore, the mean eruption time is
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