Use the normal distribution of SAT critical reading scores for which the mean is 512 and the standard deviation is 123. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 600? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? (a) Approximately % of the SAT verbal scores are less than 600. (Round to two decimal places as needed.) (b) You would expect that approximately SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.)
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!
![**SAT Verbal Scores and Normal Distribution Analysis**
Use the normal distribution of SAT critical reading scores for which the mean is 512 and the standard deviation is 123. Assume the variable \( x \) is normally distributed.
(a) What percent of the SAT verbal scores are less than 600?
(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550?
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(a) Approximately [ ]% of the SAT verbal scores are less than 600.
(Round to two decimal places as needed.)
(b) You would expect that approximately [ ] SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff80291e3-aec2-4ea4-a98f-bb850a0459e0%2Fc01c8ff5-0a03-4708-b02c-7ed1e1388426%2Fo8vsd8_processed.png&w=3840&q=75)
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