Use the normal distribution of SAT critical reading scores for which the mean is 509 and the standard deviation is 105. Assume the variable x is normally distributed (a) What percent of the SAT verbal scores are less than 650? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? (a) Approximately 90.99 % of the SAT verbal scores are less than 650. (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!
![**Understanding SAT Verbal Scores Using the Normal Distribution**
Given the normal distribution of SAT critical reading scores, with a mean of 509 and a standard deviation of 105, we will examine two questions related to the scores. Assume the variable \( x \) is normally distributed.
**(a) Determining the Percentage of Scores Below 650:**
*Question:*
What percent of the SAT verbal scores are less than 650?
*Answer:*
Approximately 90.99% of the SAT verbal scores are less than 650.
(Round to two decimal places as needed.)
**(b) Estimating Scores Greater Than 550:**
*Question:*
If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550?
*Answer:*
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%2F6c594194-a927-4ce3-85cb-dd1364b757e9%2Fd2fb7af2-3c23-43b3-8821-b1d403158f16%2Fosp30p2_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 17 images
