Scores on the Wechsler-Adult Intelligence Scale for one age group has a bell shaped distribution with a mean of 110 points and a standard deviation of 25 points. Give an interval within which about 95% of the scores fall. What score will place a person in this age group in the lower 2.5% of the population?
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!
Scores on the Wechsler-Adult Intelligence Scale for one age group has a bell shaped distribution with a
- Give an interval within which about 95% of the scores fall.
- What score will place a person in this age group in the lower 2.5% of the population?
We know that if X follows normal distribution with mean and variance , then
standardization gives:
Z= follows standard normal distribution with mean 0 and variance 1.
Also, by standard normal distribution tables, we get :
P[Z-1.96]=0.025, and due to symmetry of the normal distribution, we have:
P[Z1.96]=0.025,
so
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