The UM Ross School of Business has 300 students who graduate with a bachelor’s degree each year. A random sample of students was selected, and their GMAT scores reported. Whether or not they were seeking admission to a graduate business school in the next year was recorded. Here is additional information that you may need to answer the questions. Total GMAT Scores are normally distributed range from 200 to 800. The current average combined GMAT score is 560, with a standard deviation of 100. Among the Ross sample, the average GMAT score was 580, with a standard deviation of 85. In the population of students graduating from Ross, 72% seek admission to a graduate business school in the next year. Make sure to use the new concepts in this module. This exercise is different from the previous standardized test exercises. It is using sample data. There is a _________ percent chance that a simple random sample of 10 applicants will provide an estimate of the population mean GMAT score that is within +/-10 of the actual population mean. There is a _________ percent chance that a simple random sample of 30 applicants will provide an estimate of the population mean GMAT score that is within +/-10 of the actual population mean. There is a _________ percent chance that the sample mean will be higher than 600. There is a _________ percent chance that the sample mean will be between 580 and 620. There is a _________ percent chance that the sample mean will be at least 530.
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!
Exercises
- The UM Ross School of Business has 300 students who graduate with a bachelor’s degree each year. A random sample of students was selected, and their GMAT scores reported. Whether or not they were seeking admission to a graduate business school in the next year was recorded.
Here is additional information that you may need to answer the questions.
- Total GMAT Scores are
normally distributed range from 200 to 800. The current average combined GMAT score is 560, with a standard deviation of 100. - Among the Ross sample, the average GMAT score was 580, with a standard deviation of 85.
- In the population of students graduating from Ross, 72% seek admission to a graduate business school in the next year.
Make sure to use the new concepts in this module. This exercise is different from the previous standardized test exercises. It is using sample data.
- There is a _________ percent chance that a simple random sample of 10 applicants will provide an estimate of the population
mean GMAT score that is within +/-10 of the actual population mean.
- There is a _________ percent chance that a simple random sample of 30 applicants will provide an estimate of the population mean GMAT score that is within +/-10 of the actual population mean.
- There is a _________ percent chance that the sample mean will be higher than 600.
- There is a _________ percent chance that the sample mean will be between 580 and 620.
- There is a _________ percent chance that the sample mean will be at least 530.
- There is a _________ percent chance that a simple random sample of 100 applicants will provide an estimate of the population mean GMAT score that is within +/-10 of the actual population mean.
- There is a _________ percent chance that a simple random sample of 100 applicants will provide an estimate of the population mean GMAT score that is within +/-20 of the actual population mean.
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