The Weschler Intelligence Scale (IQ) for Children is approximately normally distributed with a mean of 100 and a standard deviation of 15. a) What is the probability that a randomly selected child has an IQ score above 120? b) What is the probability that a randomly selected child has an IQ score between 93 and 110? c) What IQ score would place a child in the top 3% of all IQ scores? d) What would be the range of scores that represent the middle 90% of all children's IQ score?
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!
The Weschler Intelligence Scale (IQ) for Children is approximately
a) What is the probability that a randomly selected child has an IQ score above 120?
b) What is the probability that a randomly selected child has an IQ score between 93 and 110?
c) What IQ score would place a child in the top 3% of all IQ scores?
d) What would be the
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