**Understanding SAT Critical Reading Scores Using Normal Distribution**When analyzing SAT critical reading scores, it's essential to understand how these scores are distributed. The normal distribution provides a framework for interpreting these scores. In this example, the mean SAT critical reading score is 502, with a standard deviation of 109. This guide assumes that the variable $ x $ is normally distributed.**Key Questions Explored**1. **Percent of Scores Less Than 675** - **Question (a):** What percent of the SAT verbal scores are less than 675? - **Instructions:** Use the standard normal distribution to find this percentage. 2. **Number of Scores Greater Than 575** - **Question (b):** If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? - **Instructions:** Again, employ the standard normal distribution to determine this number.To find these values, you'll need to reference the standard normal table, which provides the cumulative probabilities of a standard normal distribution.**Useful Resources**- Click here to view [page 1 of the standard normal table](#).- Click here to view [page 2 of the standard normal table](#).**Calculations**- **(a) Calculation:** - To determine the percentage of SAT verbal scores less than 675, locate the corresponding z-score using the mean and standard deviation. Round your final answer to two decimal places.- **(b) Calculation:** - For estimating the number of scores greater than 575 out of 1000, find the cumulative probability for a score less than 575 and subtract from 1 to get the probability for a score greater than 575. Multiply this probability by 1000. Round your answer to the nearest whole number.**Interactive Answer Fields**- (a) Approximately **[Fill in the blank] %** of the SAT verbal scores are less than 675. (Round to two decimal places as needed.)- (b) You would expect that approximately **[Fill in the blank]** SAT verbal scores would be greater than 575. (Round to the nearest whole number as needed.)Understanding these principles allows you to interpret and predict SAT scores using the properties of the normal distribution effectively.

Mean()=502Standard deviation()=109

Answered: Use the normal distribution of SAT…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Recently, a random sample of 25-34 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings. E Click the icon to view the frequency distribution for the amount of savings. The sample mean amount of savings is $ Frequency distribution of amount of savings (Round to the nearest dollar as needed.) The sample standard deviation is S (Round to the nearest dollar as needed.) Frequency Savings $0 $199 $200-$399 $400 $599 $600 $799 $800 $999 $1000-$1199 $1200 $1399 342 86 45 21 10 7 1 Print Done
Scores on an exam were normally distributed. Ten percent of the scores were below 60.0 and 80% were below 81. Find the mean and standard deviation of the scores. (Round the final answer for the mean to two decimal places.) (Round the final answer for the standard deviation to four decimal places.)
Use the normal distribution of SAT critical reading scores for which the mean is 514 and the standard deviation is 115. 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? Click to view page 1 of the standard normal table. LOADING... Click to view page 2 of the standard normal table. LOADING... Question content area bottom Part 1 (a) Approximately 1.181.18% of the SAT verbal scores are less than 650. (Round to two decimal places as needed.) Part 2 (b) You would expect that approximately 0.880.88 SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.)
The mean is 146 and the standard deviation is 35. A score of 41 is how many z-scores below the mean?
Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 116. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 550? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525? Click to view page 1 of the standard normal table. Click to view page 2 of the standard normal table. (a) Approximately % of the SAT verbal scores are less than 550. (Round to two decimal places as needed.)
The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each sample data set. What can you conclude? Standard deviation CV = • 100% Mean E Click the icon to view the data sets. Data Table ..... CVneights = 71.2% (Round to the nearest tenth as needed.) Heights Weights 68 181 77 169 72 167 72 207 71 177 70 175 78 185 69 186 67 221 70 216 67 209 73 206
In a normal curve, the percentage of the scores between one and two standard deviations above the mean is approximately __________. Select one: a. 14% b. 50% c. It is impossible to tell. d. 2% Clear my choice
The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each sample data set. What can you conclude? Standard deviation CV = • 100% Mean E Click the icon to view the data sets. Data Table C/heights = 5.0 % (Round to the nearest tenth as needed.) Heights Weights CVweights =% (Round to the nearest tenth as needed.) 68 181 77 169 72 167 72 207 71 177 70 175 78 185 69 186 67 221 70 216 67 209 73 206
Use the sample statistics to test the claim that the mean score on a final exam is more than 78. x¯=81x¯=81 s=10s=10 n=41
Use the normal distribution of SAT critical reading scores for which the mean is 504 and the standard deviation is 114. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 550? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525? Click to view page 1 of the standard normal table. Click to view page 2 of the standard normal table. ww (a) Approximately % of the SAT verbal scores are less than 550. 745 (Round to two decimal places as needed.) 725229 Check answer ct:

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