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Goshia [24]
3 years ago
5

A normal distribution curve, where x = 70 and σ = 15, was created by a teacher using her students’ grades. What information abou

t their performances can be obtained by analyzing the curve?
Mathematics
2 answers:
quester [9]3 years ago
5 0
The curve is a normal distribution curve where x = 70 and <span>σ = 15. The variable x is the mean of the students' grades which is equal to 70. The standard deviation is 15, the actual mean is 70+-15. A normally distributed curve means that most of the students got mostly 75. </span>
alexira [117]3 years ago
4 0

The <em><u>correct answer</u></em> is:

We can conclude that 68% of the scores were between 55 and 85; 95% of the scores were between 40 and 100; and 99.7% of the scores were between 25 and 100.

Explanation:

The empirical rule tells us that in a normal curve, 68% of data lie within 1 standard deviation of the mean; 95% of data lie within 2 standard deviations of the mean; and 99.7% of data lie within 3 standard deviations of the mean.

The mean is 70 and the standard deviation is 15. This means 1 standard deviation below the mean is 70-15 = 55 and one standard deviation above the mean is 70+15 = 85. 68% of data will fall between these two scores.

2 standard deviations below the mean is 70-15(2) = 40 and two standard deviations above the mean is 70+15(2) = 100. 95% of data will fall between these two scores.

3 standard deviations below the mean is 70-15(3) = 25 and three standard deviations above the mean is 70+15(3) = 115. However, a student cannot score above 100%; this means 99.7% of data fall between 25 and 100.

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