Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places. If your answer is negative use “minus sign”. Answer only D and E (a) What percentage of students have an SAT math score greater than 615? 16 % (b) What percentage of students have an SAT math score greater than 715? 2.5% (c) What percentage of students have an SAT math score between 415 and 515? 34% (d) What is the z-score for student with an SAT math score of 620? (e) What is the z-score for a student with an SAT math score of 405?
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!
Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the
If required, round your answers to two decimal places. If your answer is negative use “minus sign”.
Answer only D and E
| (a) | What percentage of students have an SAT math score greater than 615? |
| 16 % | |
| (b) | What percentage of students have an SAT math score greater than 715? |
| 2.5% | |
| (c) | What percentage of students have an SAT math score between 415 and 515? |
| 34% | |
| (d) | What is the z-score for student with an SAT math score of 620? |
| (e) | What is the z-score for a student with an SAT math score of 405? |
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