Summer high temperatures are distributed normally with a mean of 93.5 and a standard deviation of 3. NOTE: Round your z – score to 2 decimal places before calculating a probability. What is the summer high temperature that is the 84th percentile of this distribution? O 96.5 O91 O 90.5 O 96 O None of the above What is the probability that a randomly selected summer day has a high temperature of 96? 0 0.7967 0.2033 What is the probability that a randomly selected summer day has a high temperature greater than 96? 0 0.7967 00 01 0.2033 What is the probability that a randomly selected group of 22 summer days have an average high temperature greater than 96? 0.2033 01 0.7967
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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