We appreciate your visit to The Graduate Management Admission Test GMAT is a standardized exam used by many universities as part of the assessment for admission to graduate study in. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
This question is about the percentage of GMAT scores in specific ranges given mean and standard deviation. The answer involves calculating z-scores for given scores and using a Z-table to determine the percentage of scores within the ranges.
Explanation:
This question revolves around the concepts of mean, standard deviation, and z-score in the context of GMAT score distribution. (a) A GMAT score of 647 is 1 standard deviation above the mean as 647-547=100=1×standard deviation. To find the percentage of scores above 647, you need to look at a z-table. The value corresponding to z=1 is 0.8413, which means about 84.13% of scores fall below 647.
Hence, 100%-84.13% = 15.87% of GMAT scores are 647 or higher. Similarly, (b) A score of 747 is 2 standard deviations from the mean and according to the Z-table, 97.72% of scores fall below 747. So 100% - 97.72%=2.28% of GMAT scores are 747 or higher. (c) For scores between 347 and 547, we notice that these are -2 and 0 standard deviations from the mean, covering about 50% (from z=0) + 47.72% (from z=-2) = 97.72% of the distribution. (d) For scores between 447 and 747, these are -1 and 2 standard deviations from the mean. From a Z-table, these z-values correspond to 84.13% + (100%-97.72%) = 86.41% of the distribution.
Learn more about GMAT scores here:
https://brainly.com/question/30430021
#SPJ12
Thanks for taking the time to read The Graduate Management Admission Test GMAT is a standardized exam used by many universities as part of the assessment for admission to graduate study in. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
(a) Approximately 31.73% of GMAT scores are 647 or higher.
(b) Approximately 15.87% of GMAT scores are 747 or higher.
(c) Approximately 34.13% of GMAT scores are between 347 and 547.
(d) Approximately 68.26% of GMAT scores are between 447 and 747.
To solve these problems, we need to use the concept of z-scores, which measure the number of standard deviations a data point is from the mean. We can then use a standard normal distribution table or a calculator to find the corresponding percentages.
(a) To find the percentage of GMAT scores that are 647 or higher, we need to calculate the z-score for 647. The formula for the z-score is (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, x = 647, μ = 547, and σ = 100. Plugging these values into the formula, we get (647 - 547) / 100 = 1. Using a standard normal distribution table or calculator, we find that the area to the right of z = 1 is approximately 0.1587. To get the percentage, we multiply this by 100, resulting in approximately 15.87%. However, since we want the percentage for scores 647 or higher, we need to subtract this from 100, giving us approximately 100 - 15.87 = 84.13%.
(b) Similarly, to find the percentage of GMAT scores that are 747 or higher, we calculate the z-score for 747 using the same formula. With x = 747, μ = 547, and σ = 100, we have (747 - 547) / 100 = 2. Using the standard normal distribution table or calculator, we find that the area to the right of z = 2 is approximately 0.0228. Multiplying this by 100, we get approximately 2.28%. Subtracting this from 100, we find that approximately 100 - 2.28 = 97.72% of GMAT scores are below 747.
(c) To determine the percentage of GMAT scores between 347 and 547, we need to calculate the z-scores for both values. For 347, the z-score is (347 - 547) / 100 = -2, and for 547, the z-score is (547 - 547) / 100 = 0. Using the standard normal distribution table or calculator, we find the area to the right of z = -2 is approximately 0.9772 and the area to the right of z = 0 is 0.5. Subtracting these two values, we obtain approximately 0.9772 - 0.5 = 0.4772. Multiplying this by 100, we get approximately 47.72%.
(d) Finally, to find the percentage of GMAT scores between 447 and 747, we calculate the z-scores for both values. For 447, the z-score is (447 - 547) / 100 = -1, and for 747, the z-score is (747 - 547) / 100 = 2. Using the standard normal distribution table or calculator, we find the area to the right of z = -1 is approximately 0.8413, and the area to the right of z = 2 is approximately 0.0228. Subtracting these two values, we obtain approximately 0.8413 - 0.0228 = 0.8185. Multiplying this by 100, we get approximately 81.85%. However, since we want the percentage between the two scores, we subtract this from 100, resulting in approximately 100 - 81.85 = 18.15%.
In summary, approximately 31.73% of GMAT scores are 647 or higher, 15.87% are 747 or higher, 34.13% are between 347 and 547, and 68.26% are between 447 and 747.
Learn more about percentage here:
https://brainly.com/question/29306119
#SPJ11
