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Answer :
Approximately 21.37% of people received a failing grade (less than 65) in the statistics class. The approximate percentage of people who received a grade between 70 and 91 is 43.77%.
To calculate the percentage of people who received a grade between 70 and 91, we need to find the area under the normal distribution curve between these two grades. We can convert the grade values into z-scores using the formula z = (x - μ) / σ, where x is the grade, μ is the mean, and σ is the standard deviation.
For the lower bound of 70:
z = (70 - 68) / 15 ≈ 0.133
For the upper bound of 91:
z = (91 - 68) / 15 ≈ 1.533
Using a standard normal distribution table or a calculator, we can find the area under the curve between these two z-scores, which represents the percentage of people within that grade range. The approximate percentage is 43.77%.
To calculate the percentage of individuals who received a score with a t-score of -70 or less, we need to find the area under the t-distribution curve to the left of -70. However, we need more information about the t-distribution, such as the degrees of freedom, to determine the exact percentage. The degrees of freedom depend on the sample size and the specific context of the problem. Without that information, we cannot provide an accurate answer. Similarly, to determine the grade required to be in the top 30 percent or the 10 percent, we need more information about the distribution of grades, such as the specific shape and characteristics of the distribution. Without additional information, we cannot provide precise grades needed to meet those percentiles.
Learn more about percentiles here: brainly.com/question/1594020
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