If the set of marks on a statistics examination are approximately normally
distributed with a mean of 74 and a standard deviation of 7.9, fond
a. The lowest passing mark if the lowest 10% of students are given F‘s
b. The lowest mark to get grade A if the top 5% students are given A‘s
Answers
Answer :
The lowest passing mark is 67 and the lowest mark to get grade A is 82.
Explanation :
A normal distribution is a type of probability distribution that can be represented by a bell-shaped curve, with the majority of the data points clustering around the mean. In this case, the mean of the marks on a statistics examination is 74 and the standard deviation is 7.9.
To find the lowest passing mark, we can use the concept of standard deviation. Since the lowest 10% of students are given F's, we can use the formula for the z-score to find the number of standard deviations away from the mean that corresponds to the lowest passing mark. If we know that 84% of the data falls within 1 standard deviation from the mean, we can assume that 90% falls within 1.28 standard deviations from the mean. Therefore, the lowest passing mark would be 74 - (7.9*1.28) = 67.
To find the lowest mark to get grade A, we can use the same concept. Since the top 5% of students are given A's, we can use the z-score formula to find the number of standard deviations away from the mean that corresponds to the lowest A grade. If we know that 95% of the data falls within 1.96 standard deviations from the mean, we can assume that the lowest A grade would be 74 + (7.9*1.96) = 82.
To summarize, if the set of marks on a statistics examination are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, the lowest passing mark would be 67 and the lowest mark to get grade A would be 82.
To know more about the concept please go through the links :
https://brainly.in/question/10520350
https://brainly.in/question/13470363
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