A waitress believes the distribution of her tips has a model that is slightly skewed to the left, with a mean of $8.40 and a standard deviation of $5.30. She usually waits on about 30 parties over a weekend of work. a) Estimate the probability that she will earn at least $300. b) How much does she earn on the best 10% of such weekends? a) P(tips from 30 parties > $300) = (Round to four decimal places as needed.) b) The total amount that she earns on the best 10% of such weekends is at least $ (Round to two decimal places as needed.)
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!
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