8. In a statistics class, the average grade on the final examination was 75 with a standard deviation of 5.
a. 
Use Chebyshev’s theorem to answer: At least what percentage of the students received grades between 50 and 100?

b. 
What is the zscore for a student who had an examination score of 91? 
c. Would the test score from part b., be considered an outlier? Explain.
9. Assume we have a symmetric or bell shaped distribution. Using the Empirical Rule, about what percentage of the data falls between 3 and 1 standard deviation?
Que.8
a.
We want probability that P(50< X < 100).
Here
And according to Chebyshev's theorem, we know that approximately 99.7% of observation will lie between 3 standard deviation below and above from mean.
We see that 50 is less than 60 and 100 is greater than 90, which cover complete 3 sigma range, hence probability that P(50< X < 100) is at least 0.997.
b.
c.
Yes this is considered as outlier because it fall above 3 sigma = 3 (for standard normal distribution).
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