Question

Questions 3-6. Professor Ivy gives a test and finds that she has a Mean of 74 with a standard deviation of 8 for her class.

Answer 1

In the test that Professor Ivy gives, the score has Mean of 74 with a standard deviation of 8. I can't solve no.3 because you didn't upload curve

There is a rule called "68-95-99.7" rule in normal distribution statistic. These 3 numbers represent the percentage of data that are within 1-3 z score from the mean respectively. 

4. The middle 68% of the class would score between what two values (what range of scores)?
Data of middle 68% will be 34% above the mean and 34% below the mean. If you see the Z-score table, 34% above the mean(50%+34%=84%) that has 0.84 value would be Z=1. The same with 34% below the mean, Z=-1.
Then, the data range would be:
range= score mean  +/- (Z-score * standard deviation)
range= 74 +/- (1*8)
range= 74 +/- 8= 66-82


5. 99.7% of the students would have test scores between what two values (what range of scores)?
Data of middle 99.7% will be 49.85% above the mean and 49.85% below the mean. If you see the Z-score table, 49.85%  above the mean(50%+49.85% =99.85%) that has 0.985 value would be around Z=3. The same with 49.85% below the mean, Z=-3.
range= score mean  +/- (Z-score * standard deviation)
range= 74 +/- (3*8)
range= 74 +/- 24= 50-98

6. Write a sentence using the 99.7% range.

The data range of 99.7% could be interpreted these ways:
Around 99.7% of the student will have a score between 50-98.
If you pick a random student score, there is 99.7% that the score is between 50-98.