3.7 LA weather, Part I: The average daily high temperature in June in LA is 78°F with a standard deviation of 5°F. Suppose that the temperatures in June closely follow a normal distribution. a) What is the probability of observing an 84°F temperature or higher in LA during a randomly chosen day in June? Round your answer to 4 decimal places. b) How cool are the coldest 10% of the days (days with lowest average high temperature) during June in LA? Round your answer to 1 decimal place.
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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