17. To find the 90th percentile of all ACT scores (the score that separates the bottom...

 

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17. To find the 90th percentile of all ACT scores (the score that separates the bottom 90% from the top 10% of all ACT scores), follow the steps below. Step 1: Find the z-score that has 90% area to the left under the standard normal curve by finding the proportion closest to 0.9000 in the standard normal table and write the corresponding z-score or type qnorm(0.90) in RStudio and write the result here x-u Step 2: Then use the formula z = - *" to find x by plugging in the z-score, μ, and othen solving for x. This score is the 90th percentile of all scores. 18. The "68-95-99.7 rule" means that for all normal distributions, approximately 68% of ob- servations are within 1 standard deviation of the mean, 95% are within two standard devia- tions, and 99.7% are within 3 standard deviations. This is also called the Empirical Rule. a. To find an interval containing approximately 68% of all ACT scores, add and subtract the standard deviation of 5.1 from the mean of 21.1 and write the resulting interval: b. To find an interval containing approximately 95% of all ACT scores, add and sub- tract two standard deviations from the mean of 21.1 and write the resulting interval: c. Use the same procedure to find an interval containing approximately 99.7% of all ACT scores. 17. To find the 90th percentile of all ACT scores (the score that separates the bottom 90% from the top 10% of all ACT scores), follow the steps below. Step 1: Find the z-score that has 90% area to the left under the standard normal curve by finding the proportion closest to 0.9000 in the standard normal table and write the corresponding z-score or type qnorm(0.90) in RStudio and write the result here x-u Step 2: Then use the formula z = - *" to find x by plugging in the z-score, μ, and othen solving for x. This score is the 90th percentile of all scores. 18. The "68-95-99.7 rule" means that for all normal distributions, approximately 68% of ob- servations are within 1 standard deviation of the mean, 95% are within two standard devia- tions, and 99.7% are within 3 standard deviations. This is also called the Empirical Rule. a. To find an interval containing approximately 68% of all ACT scores, add and subtract the standard deviation of 5.1 from the mean of 21.1 and write the resulting interval: b. To find an interval containing approximately 95% of all ACT scores, add and sub- tract two standard deviations from the mean of 21.1 and write the resulting interval: c. Use the same procedure to find an interval containing approximately 99.7% of all ACT scores.

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Solution Q17 Step1 By using Rstudio Zscoreqnorm090Zscore ... View the full answer