Question

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 z-score 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?

Answer 1

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).