A variable is normally distributed with mean 8 and standard deviation 2. a. Determine the quartiles of the variable. b. Obtain and interpret the 80th percentile. c. Find the value that​ 65% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025.  Interpret the answer.   c. The value that​ 65% of all possible values of the variable exceed is ______. ​(Round to two decimal places as​ needed.)   d. The two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025 are ___________ and ____________. ​(Round to two decimal places as needed. Use ascending​ order.)   These values enclose the area of the normal curve that is within _________ standard deviations. ​(Round to the nearest integer as​ needed.)

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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!