Because P(z < 0.44) = 0.67, 67% of all z values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution. (Hint: If the cumulative area that you must look for does not appear in the z table, use the closest entry. Round all answers to two decimal places.) (a) The 97.5th percentile = (Hint: Look for area 0.9750.) (b) The 70.2th percentile =
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!
Because P(z < 0.44) = 0.67, 67% of all z values are less than 0.44, and 0.44 is the 67th percentile of the standard
(a) The 97.5th percentile = (Hint: Look for area 0.9750.)
(b) The 70.2th percentile =
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