68 - 95 - 99.7% Rule and Percentiles

6. 125 students took a 100-point midterm. The mean for the test was 66.5 points, with a standard deviation of 5.2 points. The results formed an almost perfectly normal distribution.

a. Generally speaking, what is the range of typical values for normally distributed data? b. Calculate the range of what you would consider "typical" and explain why you are

choosing that interval. c. Are the overall exam results consistent? How can you tell? d. Was this a difficult test? How can you tell?

Hint: for the next three problems, use z-scores and the percentile table to analyze the scenarios.

Is it possible that a student scored better than 90 points on the test? Justify your answer.

What is the probability that a student scored better than 90 points on the test?

What is the probability that a student score worse than 90 points on the test?