A math teacher’s midterm is worth 200 points. The mean of the test is 143 and the standard deviation is 15.7. If the scores have
a bell shaped distribution, what percentage of the scores are between 111.6 and 174.4?
A. About 99.7%
B. About 68%
C. About 62.8%
D. About 95%
2 answers:
The answer is D: about 95%.
Answer with explanation:
Mean,

Standard Deviation 
Total Population = 200
Formula for Z Score and calculation of two Z scores.

Similarly,

So the two values that is , 111.6 and 174.4 , lies 2 standard deviation on left and 2 standard deviation on the right of mean.
→With the Help of Z table, the conclusion can be drawn that, 95 % of Data will lie within two standard deviation that is above and Below the Mean.
Option D: About 95%
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