Two students are taking a college entrance exam and known to have a normal distribution of scores. Both students receive raw scores of 60 and 97, which correspond to z scores (often called the standardized scores) of -1.5 and 3 respectively. 1 Denote the normal probability distribution of the raw exam scores. 2 Calculate the value of mean for the distribution of raw exam scores. 3 Calculate the value of standard deviation of the raw exam scores.
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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