Math/ Bell Curve question W/ standard deviation?

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Guillermo

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X: score of the students

X -- n(75; 5)

P(X > 80) = P((X - 75)/5 > (80 - 75)/5) = P(Z > 1) = 0.1587* 300 ? 48

P(X < 65) = P((X - 75)/5 > (65 - 75)/5) = P(Z < - 2) = 0.0228*300 ? 7
 
Assuming a Normal Distribution, 68% of data is within 1 SD of the mean, and 95% is within 2 SDs of the mean.

The mean is 75 and SD is 5. So 68% of data is between 70 and 80. Then 100% - 68% = 34% is either less than 70, or greater than 80. The Normal Distribution is symmetrical, so half of the 34%, or 17%, is greater than 80. 300*17% = 51.

95% of data is between 65 and 85. Then 100% - 95% = 5% is either less than 65 or greater than 85. The Normal Distribution is symmetrical, so half of the 5%, or 2.5% is less than 65. 300*2.5% = 7.5, round to 8
 
I gave a test to 300 students and the average score was a 75, each SD was 5 points....tell me, how many students will score above an 80 and how many below a 65? Can someone explain this to me?
 
Assuming a Normal Distribution, 68% of data is within 1 SD of the mean, and 95% is within 2 SDs of the mean.

The mean is 75 and SD is 5. So 68% of data is between 70 and 80. Then 100% - 68% = 34% is either less than 70, or greater than 80. The Normal Distribution is symmetrical, so half of the 34%, or 17%, is greater than 80. 300*17% = 51.

95% of data is between 65 and 85. Then 100% - 95% = 5% is either less than 65 or greater than 85. The Normal Distribution is symmetrical, so half of the 5%, or 2.5% is less than 65. 300*2.5% = 7.5, round to 8
 
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