Chapter 07, Section 7.4, Problem 038c The amounts of electricity bills for all households in a city have a skewed probability distribution with a mean of $137 and a standard deviation of $30. Find the probability that the mean amount of electric bills for a random sample of 75- households selected from this city will be more than the population mean by at least $4. Round your answer to four decimal places. P (x greater than µ by at least $4) =

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Q: Chapter 07, Section 7.4, Problem 038c The amounts of electricity bills for all households in a city…

A: Given: x=137, σ=30, n=75

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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!