2) IQ scores are normally distributed with mean 100 and standard deviation 16. a) Calculate the probability that a randomly chosen individual has IQ more than 120 b) Calculate the probability that a randomly chosen group of 25 people has average IQ more than 120. 3) Grades on a Statistics Final exam are normally distributed with mean 70 and standard deviation 15. Calculate the probability that a random sample of size 25 will produce an ayerage less than 80
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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