A family’s utility costs are as follows: Electricity: $0.13 per kWh Propane gas: $2.30 per gallon Their monthly usage fluctuates. Assume both are normally distributed with mean and standard deviations Electricity: μ = 850 kWh, σ = 100 kWh Propane gas: μ = 55 gallons, σ = 6 gallons Let Y = the monthly utility cost d) the probability that the monthly cost of electricity is greater than the monthly cost of propane gas
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!
A family’s utility costs are as follows:
Electricity: $0.13 per kWh
Propane gas: $2.30 per gallon
Their monthly usage fluctuates. Assume both are
deviations
Electricity: μ = 850 kWh, σ = 100 kWh
Propane gas: μ = 55 gallons, σ = 6 gallons
Let Y = the monthly utility cost
d) the probability that the monthly cost of electricity is greater than the monthly cost of propane gas
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