The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT, What proportion have SAT scores less than 350? What proportion have SAT scores greater than 750? What is the minimum SAT score needed to be in the highest 10% of the population? If the state college only accepts students from the top 15% of the SAT distribution, what is the minimum SAT score needed to be accepted?
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 distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT,
- What proportion have SAT scores less than 350?
- What proportion have SAT scores greater than 750?
- What is the minimum SAT score needed to be in the highest 10% of the population?
- If the state college only accepts students from the top 15% of the SAT distribution, what is the minimum SAT score needed to be accepted?
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