To answer the question, we can use the properties of the normal distribution and z-scores. Here are the correct statements:
A. The area under the curve between 80 and 90 is 0.68.
C. The area under the curve between 75 and 90 is 0.95.
Step-by-step explanation:
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and about 95% falls within two standard deviations.
Using these properties, we can determine the correct statements:
A. The area under the curve between 80 and 90 is 0.68. This is correct because the range from 80 to 90 is within one standard deviation of the mean, which covers about 68% of the data.
C. The area under the curve between 75 and 90 is 0.95. This is correct because the range from 75 to 90 is within two standard deviations of the mean, which covers about 95% of the data.
Therefore, statements A and C are correct.