Shower temperature at the Oxnard Health Club showers is regulated automatically. The heater kicks in when the temperature falls to 99ºF and shuts off when the temperature reaches 107ºF. Water temperature then falls slowly until the heater kicks in again. At a given moment, the water temperature is a uniformly distributed random variable U(99,107). (a) Find the mean temperature. (Round your answer to 1 decimal place.) Mean degrees (b) Find the standard deviation of the temperature. (Round your answer to 4 decimal places.) Standard deviation degrees (c) Find the 75th percentile for water temperature. (Round your answer to 2 decimal places.) 75th percentile degrees
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!
Shower temperature at the Oxnard Health Club showers is regulated automatically. The heater kicks in when the temperature falls to 99ºF and shuts off when the temperature reaches 107ºF. Water temperature then falls slowly until the heater kicks in again. At a given moment, the water temperature is a uniformly distributed random variable U(99,107).
(a) Find the mean temperature. (Round your answer to 1 decimal place.)
Mean degrees
(b) Find the standard deviation of the temperature. (Round your answer to 4 decimal places.)
Standard deviation degrees
(c) Find the 75th percentile for water temperature. (Round your answer to 2 decimal places.)
75th percentile degrees
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